Chapter 5-Quantum mechanics
Feynman 费曼物理学讲义英文版 2至5章
2Basic Physics2–1IntroductionIn this chapter, we shall examine the most fundamental ideas that we have about physics—the nature of things as we see them at the present time. We shall not discuss the history of how we know that all these ideas are true; you will learn these details in due time.The things with which we concern ourselves in science appear in myriad forms, and with a multitude of attributes. For example, if we stand on the shore and look at the sea, we see the water, the waves breaking, the foam, the sloshing motion of the water, the sound, the air, the winds and the clouds, the sun and the blue sky, and light; there is sand and there are rocks of various hardness and permanence, color and texture. There are animals and seaweed, hunger and disease, and the observer on the beach; there may be even happiness and thought. Any other spot in nature has a similar variety of things and influences. It is always as complicated as that, no matter where it is. Curiosity demands that we ask questions, that we try to put things together and try to understand this multitude of aspects as perhaps resulting from the action of a relatively small number of elemental things and forces acting in an infinite variety of combinations.For example: Is the sand other than the rocks? That is, is the sand perhaps nothing but a great number of very tiny stones? Is the moon a great rock? If we understood rocks, would we also understand the sand and the moon? Is the wind a sloshing of the air analogous to the sloshing motion of the water in the sea? What common features do different movements have? What is common to different kinds of sound? How many different colors are there? And so on. In this way we try gradually to analyze all things, to put together things which at first sight look different, with the hope that we may be able to reduce the number of different things and thereby understand them better.A few hundred years ago, a method was devised to find partial answers to such questions. Observation, reason, and experiment make up what we call the scientific method. We shall have to limit ourselves to a bare description of our basic view of what is sometimes called fundamental physics, or fundamental ideas which have arisen from the application of the scientific method.What do we mean by ―understanding‖ something? We can imagine that this complicated array of moving things which constitutes ―the world‖ is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch on to a few of the rules. The rules of the game are what we mean by fundamental physics. Even if we knew every rule, however, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited. If you play chess you must know that it is easy to learn all the rules, and yet it is often very hard to select the best move or to understand why a player moves as he does. Soit is in nature, only much more so; but we may be able at least to find all the rules. Actually, we do not have all the rules now. (Every once in a while something like castling is going on that we still do not understand.) Aside from not knowing all of the rules, what we really can explain in terms of those rules is very limited, because almost all situations are so enormously complicated that we cannot follow the plays of the game using the rules, much less tell what is going to happen next. We must, therefore, limit ourselves to the more basic question of the rules of the game. If we know the rules, we consider that we ―understand‖ the world.How can we tell whether the rules which we ―guess‖ at are really right if we cannot analyze the game very well? There are, roughly speaking, three ways. First, there may be situations where nature has arranged, or we arrange nature, to be simple and to have so few parts that we can predict exactly what will happen, and thus we can check how our rules work. (In one corner of the board there may be only a few chess pieces at work, and that we can figure out exactly.)A second good way to check rules is in terms of less specific rules derived from them. For example, the rule on the move of a bishop on a chessboard is that it moves only on the diagonal. One can deduce, no matter how many moves may be made, that a certain bishop will always be on a red square. So, without being able to follow the details, we c an always check our idea about the bishop’s motion by finding out whether it is always on a red square. Of course it will be, for a long time, until all of a sudden we find that it is on a black square (what happened of course, is that in the meantime it was captured, another pawn crossed for queening, and it turned into a bishop on a black square). That is the way it is in physics. For a long time we will have a rule that works excellently in an over-all way, even when we cannot follow the details, and then some time we may discover a new rule. From the point of view of basic physics, the most interesting phenomena are of course in the new places, the places where the rules do not work—not the places where they do work! That is the way in which we discover new rules.The third way to tell whether our ideas are right is relatively crude but probably the most powerful of them all. That is, by rough approximation. While we may not be able to tell why Alekhine moves this particular piece, perhaps we can roughly understand that he is gathering his pieces around the king to protect it, more or less, since that is the sensible thing to do in the circumstances. In the same way, we can often understand nature, more or less, without being able to see what every little piece is doing, in terms of our understanding of the game.At first the phenomena of nature were roughly divided into classes, like heat, electricity, mechanics, magnetism, properties of substances, chemical phenomena, light or optics, x-rays, nuclear physics, gravitation, meson phenomena, etc. However, the aim is to see complete nature as different aspects of one set of phenomena. That is the problem in basic theoretical physics, today—to find the laws behind experiment; to amalgamate these classes. Historically, we have always been able to amalgamate them, but as time goes on new things are found. We were amalgamating very well, when all of a sudden x-rays were found. Then we amalgamated some more, and mesons were found. Therefore, at any stage of the game, it always looks rathermessy. A great deal is amalgamated, but there are always many wires or threads hanging out in all directions. That is the situation today, which we shall try to describe.Some historic examples of amalgamation are the following. First, take heat and mechanics. When atoms are in motion, the more motion, the more heat the system contains, and so heat and all temperature effects can be represented by the laws of mechanics. Another tremendous amalgamation was the discovery of the relation between electricity, magnetism, and light, which were found to be different aspects of the same thing, which we call today the electromagnetic field. Another amalgamation is the unification of chemical phenomena, the various properties of various substances, and the behavior of atomic particles, which is in the quantum mechanics of chemistry.The question is, of course, is it going to be possible to amalgamate everything, and merely discover that this world represents different aspects of one thing? Nobody knows. All we know is that as we go along, we find that we can amalgamate pieces, and then we find some pieces that do not fit, and we keep trying to put the jigsaw puzzle together. Whether there are a finite number of pieces, and whether there is even a border to the puzzle, is of course unknown. It will never be known until we finish the picture, if ever. What we wish to do here is to see to what extent this amalgamation process has gone on, and what the situation is at present, in understanding basic phenomena in terms of the smallest set of principles. To express it in a simple manner, what are things made of and how few elements are there?2–2Physics before 1920It is a little difficult to begin at once with the present view, so we shall first see how things looked in about 1920 and then take a few things out of that picture. Before 1920, our world picture was something like this: The ―stage‖ on which the universe goes is the three-dimensional space of geometry, as described by Euclid, and things change in a medium called time. The elements on the stage are particles, for example the atoms, which have some properties. First, the property of inertia: if a particle is moving it keeps on going in the same direction unless forces act upon it. The second element, then, is forces, which were then thought to be of two varieties: First, an enormously complicated, detailed kind of interaction force which held the various atoms in different combinations in a complicated way, which determined whether salt would dissolve faster or slower when we raise the temperature. The other force that was known was a long-range interaction—a smooth and quiet attraction—which varied inversely as the square of the distance, and was called gravitation. This law was known and was very simple. Why things remain in motion when they are moving, or why there is a law of gravitation was, of course, not known.A description of nature is what we are concerned with here. From this point of view, then, a gas, and indeed all matter, is a myriad of moving particles. Thus many of the things we saw while standing at the seashore can immediately be connected. First the pressure: this comes from the collisions of the atoms with the walls or whatever; the drift of the atoms, if they are all moving in one direction on the average, is wind; the random internal motions are the heat. There are waves of excess density,where too many particles have collected, and so as they rush off they push up piles of particles farther out, and so on. This wave of excess density is sound. It is a tremendous achievement to be able to understand so much. Some of these things were described in the previous chapter.What kinds of particles are there? There were considered to be 92 at thattime: 92 different kinds of atoms were ultimately discovered. They had different names associated with their chemical properties.The next part of the problem was, what are the short-range forces? Why does carbon attract one oxygen or perhaps two oxygens, but not three oxygens? What is the machinery of interaction between atoms? Is it gravitation? The answer is no. Gravity is entirely too weak. But imagine a force analogous to gravity, varying inversely with the square of the distance, but enormously more powerful and having one difference. In gravity everything attracts everything else, but now imagine that there are two kinds of ―things,‖ and that this new force (which is the electrical force, of course) has the property that likes repel but unlikes attract. The ―thing‖ that carries this stron g interaction is called charge.Then what do we have? Suppose that we have two unlikes that attract each other, a plus and a minus, and that they stick very close together. Suppose we have another charge some distance away. Would it feel any attraction? It would feel practically none, because if the first two are equal in size, the attraction for the one and the repulsion for the other balance out. Therefore there is very little force at any appreciable distance. On the other hand, if we get very close with the extra charge, attraction arises, because the repulsion of likes and attraction of unlikes will tend to bring unlikes closer together and push likes farther apart. Then the repulsion will be less than the attraction. This is the reason why the atoms, which are constituted out of plus and minus electric charges, feel very little force when they are separated by appreciable distance (aside from gravity). When they come close together, they can ―see inside‖ each other and rearrange their charges, with the result that they have a very strong interaction. The ultimate basis of an interaction between the atoms is electrical. Since this force is so enormous, all the plusses and all minuses will normally come together in as intimate a combination as they can. All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out. Once in a while, by accident, we may rub off a few minuses or a few plusses (usually it is easier to rub off minuses), and in those circumstances we find the force of electricity unbalanced, and we can then see the effects of these electrical attractions.To give an idea of how much stronger electricity is than gravitation, consider two grains of sand, a millimeter across, thirty meters apart. If the force between them were not balanced, if everything attracted everything else instead of likes repelling, so that there were no cancellation, how much force would there be? There would be a force of three million tons between the two! You see, there is very, very little excess or deficit of the number of negative or positive charges necessary to produce appreciableelectrical effects. This is, of course, the reason why you cannot see the difference between an electrically charged or uncharged thing—so few particles are involved that they hardly make a difference in the weight or size of an object.With this picture the atoms were easier to understand. They were thought to have a ―nucleus‖ at the center, which is positively electrically charged and very massive, and the nucleus is surrounded by a certain number of ―electrons‖ which are very light and negatively charged. Now we go a little ahead in our story to remark that in the nucleus itself there were found two kinds of particles, protons and neutrons, almost of the same weight and very heavy. The protons are electrically charged and the neutrons are neutral. If we have an atom with six protons inside its nucleus, and this is surrounded by six electrons (the negative particles in the ordinary world of matter are all electrons, and these are very light compared with the protons and neutrons which make nuclei), this would be atom number six in the chemical table, and it is called carbon. Atom number eight is called oxygen, etc., because the chemical properties depend upon the electrons on the outside, and in fact only upon how many electrons there are. So the chemical properties of a substance depend only on a number, the number of electrons. (The whole list of elements of the chemists really could have been called 1, 2, 3, 4, 5, etc. Instead of saying ―carbon,‖ we could say ―element six,‖ meaning six electrons, but of course, when the elements were first discovered, it was not known that they could be numbered that way, and secondly, it would make everything look rather complicated. It is better to have names and symbols for these things, rather than to call everything by number.)More was discovered about the electrical force. The natural interpretation of electrical interaction is that two objects simply attract each other: plus against minus. However, this was discovered to be an inadequate idea to represent it. A more adequate representation of the situation is to say that the existence of the positive charge, in some sense, distorts, or creates a ―condition‖ in space, so that when we put the negative charge in, it feels a force. This potentiality for producing a force is called an electric field. When we put an electron in an electric field, we say it is ―pulled.‖ We then have two rules: (a) charges make a field, and (b) charges in fields have forces on them and move. The reason for this will become clear when we discuss the following phenomena: If we were to charge a body, say a comb, electrically, and then place a charged piece of paper at a distance and move the comb back and forth, the paper will respond by always pointing to the comb. If we shake it faster, it will be discovered that the paper is a little behind, there is a delay in the action. (At the first stage, when we move the comb rather slowly, we find a complication which is magnetism. Magnetic influences have to do with charges in relative motion, so magnetic forces and electric forces can really be attributed to one field, as two different aspects of exactly the same thing. A changing electric field cannot exist without magnetism.) If we move the charged paper farther out, the delay is greater. Then an interesting thing is observed. Although the forces between two charged objects should go inversely as the square of the distance, it is found, when we shake acharge, that the influence extends very much farther out than we would guess at first sight. That is, the effect falls off more slowly than the inverse square.Here is an analogy: If we are in a pool of water and there is a floating cork very close by, we can move it ―directly‖ by pushing the water with another cork. If you looked only at the two corks, all you would see would be that one moved immediately in response to the motion of the other—there is some kind of ―interaction‖ between them. Of course, what we really do is to disturb the water; the water then disturbs the other cork. We could make up a ―law‖ that if you pushed the water a little bit, an object close by in the water would move. If it were farther away, of course, the second cork would scarcely move, for we move the water locally. On the other hand, if we jiggle the cork a new phenomenon is involved, in which the motion of the water moves the water there, etc., and waves travel away, so that by jiggling, there is an influence very much farther out, an oscillatory influence, that cannot be understood from the direct interaction. Therefore the idea of direct interaction must be replaced with the existence of the water, or in the electrical case, with what we call the electromagnetic field.The electromagnetic field can carry waves; some of these waves are light, others are used in radio broadcasts, but the general name is electromagnetic waves. These oscillatory waves can have various frequencies. The only thing that is really different from one wave to another is the frequency of oscillation. If we shake a charge back and forth more and more rapidly, and look at the effects, we get a whole series of different kinds of effects, which are all unified by specifying but one number, the number of oscillations per second. The usual ―pickup‖ that we get from electric currents in the circuits in the walls of a building have a frequency of about onehundred cycles per second. If we increase the frequency to 500 or 1000 kilocycles (1 kilocycle=1000cycles) per second, we are ―on the air,‖ for this is the frequency range which is used for radio broadcasts. (Of course it has nothing to do with the air! We can have radio broadcasts without any air.) If we again increase the frequency, we come into the range that is used for FM and TV. Going still further, we use certain short waves, for example for radar. Still higher, and we do not need an instrument to ―see‖ the stuff, we can see it with the human eye. In the range offrequency from 5×1014 to 1015 cycles per second our eyes would see the oscillation of the charged comb, if we could shake it that fast, as red, blue, or violet light, depending on the frequency. Frequencies below this range are called infrared, and above it, ultraviolet. The fact that we can see in a particular frequency range makes that part of the electromagnetic spectrum no more impressive than the other parts from a physicist’s standpoint, but from a human standpoint, of course, it is more interesting. If we go up even higher in frequency, we get x-rays. X-rays are nothing but very high-frequency light. If we go still higher, we get gamma rays. These two terms, x-rays and gamma rays, are used almost synonymously. Usually electromagnetic rays coming from nuclei are called gamma rays, while those of high102 Electrical disturbanceField 5×105 – 106 Radio broadcastWaves 108 FM —TV 1010 Radar5×1014 – 1015 Light1018X-rays Particle 1021γ-rays, nuclear 1024γ-rays, ―artificial‖ 1027 γ-rays, in cosmic rays2–3Quantum physicsHaving described the idea of the electromagnetic field, and that this field cancarry waves, we soon learn that these waves actually behave in a strange way whichseems very unwavelike. At higher frequencies they behave much morelike particles! It is quantum mechanics , discovered just after 1920, which explainsthis strange behavior. In the years before 1920, the picture of space as athree-dimensional space, and of time as a separate thing, was changed by Einstein,first into a combination which we call space-time, and then still further intoa curved space-time to represent gravitation. So the ―stage‖ is changed intospace-time, and gravitation is presumably a modification of space-time. Then it wasalso found that the rules for the motions of particles were incorrect. The mechanicalrules of ―inertia‖ and ―forces‖ are wrong —Newton’s laws are wrong —in the world ofatoms. Instead, it was discovered that things on a small scale behave nothinglike things on a large scale. That is what makes physics difficult —and very interesting.It is hard because the way things behave on a small scale is so ―unnatural‖; we haveno direct experience with it. Here things behave like nothing we know of, so that it isimpossible to describe this behavior in any other than analytic ways. It is difficult, andtakes a lot of imagination.Quantum mechanics has many aspects. In the first place, the idea that a particlehas a definite location and a definite speed is no longer allowed; that is wrong. Togive an example of how wrong classical physics is, there is a rule in quantummechanics that says that one cannot know both where something is and how fast it ismoving. The uncertainty of the momentum and the uncertainty of the position are complementary, and the product of the two is bounded by a small constant. We canwrite the law like this: ΔxΔp≥ℏ/2, but we shall explain it in more detail later. This rule is the explanation of a very mysterious paradox: if the atoms are made out of plus and minus charges, why don’t the minus charges simply sit on top of the plus charges (they attract each other) and get so close as to completely cancel them out? Why are atoms so big? Why is the nucleus at the center with the electrons around it? It was first thought that this was because the nucleus was so big; but no, the nucleus is verysmall. An atom has a diameter of about 10−8 cm. The nucleus has a diameter ofabout 10−13 cm. If we had an atom and wished to see the nucleus, we would have to magnify it until the whole atom was the size of a large room, and then the nucleus would be a bare speck which you could just about make out with the eye, but very nearly all the weight of the atom is in that infinitesimal nucleus. What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy. With this energy they would break away from the nucleus. They make a compromise: they leave themselves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule. (Remember that when a crystal is cooled to absolute zero, we said that the atoms do not stop moving, they still jiggle. Why? If they stopped moving, we would know where they were and that they had zero motion, and that is against the uncertainty principle. We cannot know where they are and how fast they are moving, so they must be continually wiggling in there!) Another most interesting change in the ideas and philosophy of science brought about by quantum mechanics is this: it is not possible to predict exactly what will happen in any circumstance. For example, it is possible to arrange an atom which is ready to emit light, and we can measure when it has emitted light by picking up a photon particle, which we shall describe shortly. We cannot, however, predict when it is going to emit the light or, with several atoms, which one is going to. You may say that this is because there are some internal ―wheels‖ which we have not looked at closely enough. No, there are no internal wheels; nature, as we understand it today, behaves in such a way that it is fundamentally impossible to make a precise prediction of exactly what will happen in a given experiment. This is a horrible thing; in fact, philosophers have said before that one of the fundamental requisites of science is that whenever you set up the same conditions, the same thing must happen. This is simply not true, it is not a fundamental condition of science. The fact is that the same thing does not happen, that we can find only an average, statistically, as to what happens. Nevertheless, science has not completely collapsed. Philosophers, incidentally, say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong. For example, some philosopher or other said it is fundamental to the scientific effort that if an experimentis performed in, say, Stockholm, and then the same experiment is done in, say, Quito, the same results must occur. That is quite false. It is not necessary that science do that; it may be a fact of experience, but it is not necessary. For example, if one of the experiments is to look out at the sky and see the aurora borealis in Stockholm, you do not see it in Quito; that is a different phenomenon. ―But,‖ you say, ―that is something that has to do with the outside; can you close yourself up in a box in Stockholm and pull down the shade and get any difference?‖ Surely. If we take a pendulum on a universal joint, and pull it out and let go, then the pendulum will swing almost in a plane, but not quite. Slowly the plane keeps changing in Stockholm, but not in Quito. The blinds are down, too. The fact that this happened does not bring on the destruction of science. What is the fundamental hypothesis of science, the fundamental philosophy? We stated it in the first chapter: the sole test of the validity of any idea is experiment. If it turns out that most experiments work out the same in Quito as they do in Stockholm, then those ―most experiments‖ will be used to formulate some general law, and those experiments which do not come out the same we will say were a result of the environment near Stockholm. We will invent some way to summarize the results of the experiment, and we do not have to be told ahead of time what this way will look like. If we are told that the same experiment will always produce the same result, that is all very well, but if when we try it, it does not, then it does not. We just have to take what we see, and then formulate all the rest of our ideas in terms of our actual experience.Returning again to quantum mechanics and fundamental physics, we cannot go into details of the quantum-mechanical principles at this time, of course, because these are rather difficult to understand. We shall assume that they are there, and go on to describe what some of the consequences are. One of the consequences is that things which we used to consider as waves also behave like particles, and particles behave like waves; in fact everything behaves the same way. There is no distinction between a wave and a particle. So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one. Now it is true that when the frequency is low, the field aspect of the phenomenon is more evident, or more useful as an approximate description in terms of everyday experiences. But as the frequency increases, the particle aspects of the phenomenon become more evident with the equipment with which we usually make the measurements. In fact, although we mentioned many frequencies, no phenomenon directly involving a frequency has yet been detected above approximately 1012 cycles per second. We only deduce the higher frequencies from the energy of the particles, by a rule which assumes that the particle-wave idea of quantum mechanics is valid.Thus we have a new view of electromagnetic interaction. We have a new kind of particle to add to the electron, the proton, and the neutron. That new particle is called a photon. The new view of the interaction of electrons and photons that is electromagnetic theory, but with everything quantum-mechanically correct, is called quantum electrodynamics. This fundamental theory of the interaction of light and matter, or electric field and charges, is our greatest success so far in physics. In。
Chemistry Chapter 5
Chemistry Chapter 5 WS #1 (first four pages)Complete the worksheet while viewing the power point. Use your textbook to answer remaining questions after the power point. Some information repeats itself. Consider this the important concepts in the chapter.Name of chapter:5.1 The Development of Atomic Models1. Rutherford’s atomic model could not explaina. why _________________________________give off characteristic colors when heatedb. why objects ___________________________ first glow dull red, then yellow, then white.c. his model could not explain ____________________________________.The Bohr Model2. Bohr proposed that an electron is found only in specific circular paths, or _________, aroundthe nucleus.3. Each possible electron orbit in Bohr’s model has a fixed energy called ____________.4. A quantum of energy is the amount of energy required to move an electron_______________________________________________________________________.The Quantum Mechanical Model5. Erwin Shrodinger used math to propose the ___________________________ model.6. The quantum mechanical model determines the allowed energies an electron can have and how likely it is ___________________________________________________________________________________________________________________________.Atomic Orbitals7. An _______________________ is often thought of as a region of space in which there is a high probability of finding an electron. The s orbitals are _____________ shaped, and p orbitals are __________________ shaped.5.2 Electron Configurations8. The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called ________________________.9. Aufbau principle: electrons occupy the orbitals of _________ energy first.Pauli exclusion principle: an atomic orbital may describe at most ____________. To occupy the same orbital, two electrons must have ______________; that is, the electron spins must be paired. Hund’s rule: electrons occupy orbitals of the ______________ in a way that makes the number of electrons with the _____________ direction as large as possible.Some actual electron configurations differ from those assigned using the aufbau principle because __________sublevels are not as stable as _________ sublevels, but they are more stable than other configurations.Exceptions to the aufbau principle are due to ___________________________________ in orbitals with very similar energies.5.3 Physics and the Quantum Mechanical Model—Light10. The __________________ of a wave is the wave’s height from zero to the crest. The______________________, represented by _________, is the distance between the crests. The _________________, represented by _______, is the number of wave cycles to pass a given point per unit of time. The SI unit for cycles per second is the ___________. The speed of light is _________________. Draw a picture of a wave and label the parts.11. ___________________________________ include radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.12. When sunlight passes through a prism, the different frequencies separate into a______________ of colors. The lowest frequency and longest wavelength is _____________. The other colors in order are _____________________________________________________. Atomic Spectra and Explanation of Atomic Spectra13. When atoms absorb energy, __________ move into higher energy levels. These electrons then lose energy by ________________ when they return to lower energy levels.14. The frequencies of light emitted by an element separate into discrete lines to give the_____________________ of the element.15. When the electron has its lowest possible energy, the atom is in its _______________.16. Excitation of the electron by absorbing energy raises the atom from the ground state to an______________.17. A quantum of energy in the form of light (photon) is emitted when the electron drops back toa ___________________.18. The light emitted by an electron moving from a higher to a lower energy level has a frequency __________ proportional to the energy change of the electron.Quantum Mechanics19. Einstein proposed that light could be described as quanta of energy called ______________. The quanta behave as if they were ____________________, resulting in a dual wave-particle behavior.20. In 1924, De Broglie developed an equation that predicts that all moving objects have___________________ behavior.21. The older theory of classical mechanics, adequately describes __________________________________________________________, while the newer theory of quantum mechanics describes ___________________________________________________________________. 22. The ___________________ uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time. The very act of measuring the position of an electron changes it velocity, and makes its velocity uncertain.Review…5.2 Electron Configurations (pages 133–135)1. The ways in which electrons are arranged around the nuclei of atoms arecalled ___________________________________________ .2. In the shorthand method for writing an electron configuration, what does asuperscript stand for? What do the sum of the superscripts equal?5.3 Light (pages 138–140)1. Match each term describing waves to its definition._______ amplitude a. the distance between two crests_______ wavelength b. the wave’s height from the origin to the crest_______ frequency c. the number of wave cycles to pass a given point per unit of time Atomic Spectra (page 141)4. What happens when an electric current is passed through the gas or vapor ofan element?5. Is the following sentence true or false? Explain. The emission spectrum of an elementcan be the same as the emission spectrum of another element.An Explanation of Atomic Spectra (pages 142–143)6. What is the lowest possible energy of an electron called?7. Only electrons moving from ______________________ to______________________ energy levels lose energy and emit light.WS #2 (last two pages)Chemistry—Ch. 5 textbook problems p. 149-151 (22-26, 30, 34-35, 40, 43, 61-65, 68)22. What was inadequate about Rutherford’s model of the atom? Which subatomic particles didThomson include in the plum-pudding model of the atom?23. What did Bohr assume about the motion of electrons?24. Describe Rutherford’s model of the atom and compare it with the model proposed by hisstudent Niels Bohr.25. What is the significance of the boundary of an electron cloud?26. What is an atomic orbital?30. How many electrons are in the highest occupied energy level of these atoms?c)barium b) sodium c) aluminum d) oxygen34. Give electron configurations for atoms of these elements:a) Na b) S c) Mgd) Ne e) K35. Which of these orbital designations are invalid?a)4s b) 2d c) 3f d) 3d40. List the colors of the visible spectrum in order of increasing wavelength.43. Explain the difference between the energy lost or gained by an atom according to the laws ofclassical physics and according to the quantum model of an atom.61. Pieces of energy are known asa) isotopes b) particles c) quanta d) line spectra62. The lowest sublevel in each principal energy level is represented by the symbola) f b) p c) s d) d63. Which electron transition results in the emission of energy?a)3p to 3s b) 3p to 4p c) 2s to 2p d) 1s to 2s64. Which is the ground state configuration of a magnesium atom?a) 1s22s22p63s2b) 1s22s22p63s1 c) 1s22s23s22p6 d) 1s22s22p43s265. Explain the difference between an orbit in the Bohr model and an orbital in the quantum mechanical model of the atom.68. Orbital diagrams for the ground states of two elements are shown below. Each diagramshows something that is incorrect. Identify the error in each diagram and then draw thecorrect diagram.a. Nitrogenb. MagnesiumCh. 4 review questions_______________ discovered the electron in 1897. He sealed gases in a tube and put electricity through the tube. The result was a glowing beam, or________________ ray. By using a magnet, he showed that there were tiny_______________ charged particles moving at high speeds (corpuscles or electrons). He found that the charge-to-mass ratio of electrons did not depend on the kind of gas used or type of metal plates. Thus, electrons must be part of the atoms of all elements.Thomson’s ___________________ model suggested that atoms were a_______________ mass with _______________ charged particles within similarto a plum pudding. His student, ___________________, disproved this theory by his ____________________ experiment. He found that most alpha particles went straight through showing that an atom is mostly _______________ space. He also concluded that there is a small, dense, positively charged _______________ at the center of the atom.Ch. 5 concept questionOuter _______________ gain a quantum of energy from high temperature or high _______________ and move from the ground state to an excited state. The_______________ are not stable in this higher energy level, so they emit energy called _______________ and move back to the lower energy, or ground state. We see colors because the energy emitted is in our _______________ spectrum, which is between ________ nm and __________nm. The colors in this spectrum from lowest energy are _________________________________________________________________________________________________________________.。
应用物理专业英语English Vocabulary
Chapter 8adjacent 邻近的barrier 障碍物compensation 补偿板double slit 双缝electromagnetic 电磁的grating diffraction 光栅衍射illumination 照明，照亮，阐明intensity 强度missing order 缺级monochromatic 单色的，单频的opaque 不透明的prediction 预言prevail 优胜，主导scatter 散射speck 斑点spherical 球的，球形的substitute 替代subtend 对应于（张角）transparency 透明，透明度Chapter 9analyzer 检偏器antenna 天线arbitrary 任意的，专断的circular polarized light 圆偏振光crossed polaroids 正交偏振片eliminate 排除，消除，除去elliptical 椭圆的，省略的incident 入射的molecule 分子oscillatory 摆动的orientation 取向partially polarized 部分偏振光polaroid sheet 偏振片polarizer 起偏器preferential 优先的propagation 声波symmetry 对称性transverse 横向的，横断的unpolarized light 自然光Chapter 10 anode 阳极cathode ray 阴极射线conversion factor 变换量current-varying solenoid 载流线圈curvature 曲度cyclotron 螺旋加速器cylindrical 圆柱体differential 微分的discharge tube 放电管electric field intensity 电场强度electromotive force 电动势electric motor 电动机electromagnetic 电磁铁electrostatic 静电的field lines 场力线flux 通量ferromagnetic 铁磁性galvanometer 电流计impurity 杂质integration 积分loop 环Lorentz Force 洛伦兹力magnetic monopole 磁单极magnetron 磁控管magnetic induction磁感应强度oscillator 震荡器permanent magnet 永磁铁polarity 极性repel 排斥resistivity 电阻率spiral 螺旋的test charge 试验电荷trace 轨迹uniform electric field 匀强电场Chapter 11accidentally 偶然地antiparallel 反平行bubble chamber 气泡室compass needle 罗盘针current-varying solenoid 载流线圈deflect 偏转eddy current 涡电流electromagnetic induction 电磁感应electric current 电流episode 插曲gyroscope 回转仪induced EMF 感应电动势induced current 感应电流insulation 绝缘intuitive 直观的laminate 分成薄片monopole 单极neutron star 中子星permanent magnet 永磁铁prestige 威信positron正电子rate of change 时间变化率repel 排斥rudimentary 基础的，初步的seismograph 地震仪sinusoidal 正弦的summarize 总结symmetric 对称的tenacity 韧性transformer 变压器vicinity 临近，周围voltmeter 伏特计vortex 漩涡Chapter 12annihilation 湮没angular momentum 角动量classical 经典的classical physics 经典物理学contraction 收缩，缩减deceive 欺骗delay-controlled exponential 缓发中子控制指数disappear 不见，失踪exponential 指数的General Theory of Relativity 广义相对论inertial reference frame 惯性参考系intrinsic 固有的，内在的，本质的meter stick 米尺microscopic 微观的Newtonian 牛顿的，牛顿学说的paradox 自相矛盾者platform 平台，站台postulate 假设relativistic physics 相对论性物理学satellite 卫星simultaneity 同时性spectrum 光谱special Relativity 狭义相对论subtle 稀薄的，精巧的time dilation时间膨胀transformation 转换vacuum 真空，真空状态Chapter 13amplitude 振幅barrier penetration 势垒穿透binding energy 结合能boundary 边界classical mechanics 经典力学confine 限制cosmic rays 宇宙射线de Broglie wavederivative 派生的，导出的decay 放射性衰变dimensional 空间的，维的discrete 不连续的distribution 分布double slit 双缝duality 双重性，二象性electron cloud 电子云energy level splitting 能及分裂entangle 纠缠，卷入excited energy level 激发能级exponentially 以指数级的形式地external force 外力fission 裂变ground state 基态half-life 半衰期harmonic 谐波insulator 绝缘体infinite potential well 无限深势阱integration 积分interference pattern 干涉图样judicious 明智的kinetic 动力学的，运动的leak through 漏过macroscopic 宏观的molecular 分子的muon 介子neutron 中子nucleus 原子核nuclear fission 核子分裂out of phase 反相peak 峰phase shift 相移photon 光子piezoelectric 压电的potential barrier 势垒potential well 势阱probability 概率，几率proportional 成比例的probability density 几率密度proton 质子quantum mechanics 量子力学quantization 量子化quantum 定量，量子quantum equivalence 量子当量quantum physics 量子物理学quantum state 量子态tabletop 桌面transition 跃进，迁移trapped electron 俘获电子tunneling effect 隧道效应wave function 波函数wave-particle duality波粒二象性Chapter 14absorption 吸收acronym 字首缩略词amplification 放大aperture 孔径bumper 缓冲器，减震器carve 雕刻coherent 相干的，一致的convergence 会聚性covalent bonds 共价键density gradient 密度梯度depletion 耗散层，耗尽donor 施主，给予体energy gap 禁带energy band 能带fluorescent 荧光的helium 氦hologram 全息inelastic 无弹性的kinematic 运动学的majority 多数metastable 亚稳态的metallic 金属（性）的minority 少数mono-chromatic 单色的optical pump 光泵pentavalency 五价population inversion 粒子数反转propagation 传播rectification 整流resistivity 抵抗力，电阻率semiconductor 半导体spiraling 螺旋式spontaneous 自发的stimulate 受刺激tetravalene 四价threshold 阈值triode 三极管valance electron 价电子Chapter 15antiquark 反夸克baryon 重子boson 波色子chain reaction 链式反应deuterium 氘flavor 味fusion 聚变hadron 强子ionization 电离lepton 轻子nuclear fission 原子核裂变neutron 中子penetrate 穿透proton 质子radioactive decay 放射性衰变radioisotope 放射性同位素。
Introduction to quantum mechanics
¯ @ h (x, t) i @x
(.6)
Bounded system means that the potential renders the particle to be localized at a region of finite volume. For unbounded systems, di↵erent convention for normalization is used.
is conserved (given that the potential is time independent) and is equal to the energy. Macroscopic objects we experience in our daily life appear to be governed by the Classical Mechanics described above, and no one doubted its validity until the early 20th century. It was accepted as fact that the Classical Mechanics can describe the behavior of even the smallest particle imaginable such as electron. However, with the progress of experimental capability in the beginning of the 20th century, puzzling evidences were reported, which could not be explained by the Classical Mechanics at all. Thanks to brilliant e↵orts put forth by the pioneers such as Planck, Schr¨ odinger, Bohr, Heisenberg, Born, Pauli, Dirac, the secret of the physics governing the microscopic world, now known as Quantum Mechanics, was uncovered in the early 20th century. Three important findings that led to the formulation of QM can be summarized as follows. (i) Quantization of light energy Elight = nh⌫, where h = 6.626 ⇥ 10
Quantum entanglement
Quantum entanglementMaciej LewensteinMaciej Lewenstein has obtained his degree in Physics from Warsaw University. From 1980 he worked at the Center for Theoretical Physics of the Polish Academy of Sciences. He received his doctoral degree in 1983 at the University of Essen and habilitation in 1986 in Warsaw. He became a full Professor in Poland in 1993. In 1995 he joined “Service de Photones, Atomes et Molecules” of CEA in Saclay. In 1998 he became a full professor and a head of the quantum optics theory group at the University of Hannover. In 2005 he started a new theory group at the “Insitut de Ciencias Fotoniques” in Barcelona. His research interests include: quantum optics, quantum information and statistical physics.Chiara MacchiavelloChiara Macchiavello finished her degree in Physics in 1991 and her PhD in 1995 at the University of Pavia. She held a post-doctoral for two years at the University of Oxford. Since 1998 she has been an Assistant Professor at the University of Pavia.Her research interests include quantum information processing and quantum optics.Dagmar BrussSince 2003 Dagmar Bruss is a professor at the Institute of Theoretical Physics at the University of Duesseldorf, Germany. Her research interests include the foundations of quantum information theory, classification of entanglement and quantum optical implementations of quantum computation.AbstractEntanglement is a fundamental resource in quantum information theory. It allows performing new kinds of communication, such as quantum teleportation and quantum dense coding. It is an essential ingredient in some quantum cryptographic protocols and in quantum algorithms. We give a brief overview of the concept of entanglement in quantum mechanics, and discuss the major results and open problems related to the recent scientific progress in this field.IntroductionEntanglement is a property of the states of quantum systems that are composed of many parties, nowadays frequently called Alice, Bob, Charles etc. Entanglement expresses particularly strong correlations between these parties, persistent even in the case of large separations among the parties, and going beyond simple intuition.Historically, the concept of entanglement goes back to the famous Einstein-Podolski-Rosen (EPR) “paradox”. Einstein, who discovered relativity theory and the modern meaning of causality, was never really happy with quantum mechanics. In his opinion every reasonable physical theory should exhibit a so called local realism.Suppose that we consider two particles, one of which is sent to Alice and one to Bob, and we perform independent local measurements of “reasonable” physical observables on these particles. Of course, the results might be correlated, because the particles come from the same source. But Einstein wanted really to restrict the correlations for “reasonable” physical observables to the ones that result from statistical distributions of some hidden (i.e. unknown to us and not controlled by us) variables that characterize the source of the particles. Since quantum mechanics did not seem to produce correlations consistent with a local hidden variable (LHV) model, Einstein concluded that quantum mechanics is not a complete theory. Erwin Schrödinger, in answer to Einstein’s doubts, introduced in 1935 the term “Verschränkung” (in English “entanglement”) in order to describe these particularly strong quantum mechanical correlations.Entanglement was since then a subject of intense discussions among experts in the foundations of quantum mechanics and philosophers of science (and not only science). It took, however, nearly 30 years until John Bell was able to set the framework for experimental investigations on the question of local realism. Bell formulated his famous inequalities, which have to be fulfilled in any multiparty system described by a LHV model. Alain Aspect and coworkers in Paris have demonstrated in their seminal experiment in 1981 that quantum mechanical states violate these inequalities. Recent very precise experiments of Anton Zeilinger’s group in Vienna confirmed fully Aspect’s demonstrations. All these experiments indicate the correctness of quantum mechanics, and despite various loopholes, they exclude the possibility of LHV models describing properly the physics of the considered systems.Entanglement has become again the subject of cover pages news in the 90’s, when quantum information was born. It was very quickly realized that entanglement is one of the most important resources for quantum information processing. Entanglement is a necessary ingredient for quantum cryptography, quantum teleportation, quantum densecoding, and if not necessary, then at least a much desired ingredient for quantum computing.At the same time the theory of entanglement is related to some of the open questions of mathematics, or more precisely linear algebra and functional analysis. A solution of the entanglement problem could help to characterize the so called positive linear maps, i.e. linear transformations of positive definite operators (or physically speaking quantum mechanical density matrices, see below) into positive definite operators.Entanglement of pure statesIn quantum mechanics (QM) a state of a quantum system corresponds to a vector |Psi> in some vector space, called Hilbert space. Such states are called pure states. One of the most important properties of QM is that linear superpositions of state-vectors are also legitimate state-vectors. This superposition principle lies at the heart of the matter-wave dualism and of quantum interference phenomena.Entanglement is also a result of superposition, but in the composite space of the involved parties. Let us for the moment focus on two parties, Alice and Bob. It is then easy to define states which are not entangled. Such states are product states of the form |Φ>= |a>|b>, i.e. Alice has at her disposal |a>, while Bob has |b>. Product states obviously carry no correlations between Alice and Bob. Entangled pure states may be now defined as those which are superpositions of at least two product states, such as|Φ> = α1|a1>|b1> + α2|a2>|b2> + etc.but cannot be written as a single product state in any other basis. All entangled pure states contain strong quantum mechanical correlations, and do not admit LHV models.Entanglement of mixed states and the separability problemVerify whether a given state-vector is a product state or not is a relatively easy task. In practice, however, we often either do not have full information about the system, or are not able to prepare a desired state perfectly. In effect in everyday situations we deal practically always with statistical mixtures of pure states. There exists a very convenient way to represent such mixtures as so called density operators, or matrices. A density matrix rho corresponding to a pure state-vector |Φ> is a projector onto this state. More general density matrices can be represented as sums of projectors onto pure state-vectors weighted by the corresponding probabilities.The definition of entangled mixed states for composite systems has been formulated by Reinhard Werner from Braunschweig in 1989. In fact, this definition determines which states are not entangled. Non-entangled states, called separable states, are mixtures of pure product states, i.e. convex sums of projectors onto product vectors:ρ = Σι pi|ai>|bi><ai|<bi|, (*)where 0 ≤ pi ≤ 1 are probabilities, i.e. Σιpi= 1. The physical interpretation of thisdefinition is simple: a separable state can be prepared by Alice and Bob by using local operations and classical communication. Checking whether a given state is separable or not is a notoriously difficult task, since one has to check whether the decomposition (*) exists or not. This difficult problem is known under the name of “separability or entanglement problem”, and has been a subject of intensive studies in the recent years.Simple entanglement criteriaThe difficulty of the separability problem comes from the fact that rho admits in general an infinite number of decompositions into a mixture of some states, and one has to check whether among them there exists at least one of the form (*). One of the most powerful necessary conditions for separability has been found by one of the fathers of quantum information, the late Asher Peres. Peres (Technion, Haifa) observed that since Alice and Bob may prepare separable states using local operations, Alice may safely reverse the time arrow in her system, which will change the state, but will not produce something unphysical. In general, such a partial time reversal is not a physical operation, and can transform a density operator (which is positive definite) into an operator that is no more positive definite. In fact this is what happens with all pure entangled states. Mathematically speaking partial time reversal corresponds to partial transposition of the density matrix (only on Alice's side). We arrive in this way at the Peres criterion: If a stateρis separable then its partial transposition has to be positive definite.This criterion is usually called positive partial transpose condition, or shortly PPT condition. Amazingly, the PPT condition is not only necessary for separability, but it is also a sufficient condition for low dimensional systems such as two qubits (dimension 2x2)and a system composed of one qubit and one qutrit (dimension 2x3). In higher dimensions, starting from 2x4 and 3x3, this is no longer true: there exist entangled states with positive partial transpose, which are called PPT entangled states.There exist several other necessary or sufficient separability criteria which have been established and frequently discussed in recent years. For example, states that are close to the completely chaotic state (whose density operator is equal to the normalized identity) are necessarily separable. There exist also other criteria that employ entropic inequalities, uncertainty relations, or an appropriate reordering of the density matrix (so called realignment criterion) etc. There exists, however, no general simple operational criterion of separability that would work in systems of arbitrary dimension.Entanglement witnessesThe set of all states P is obviously compact and convex. If ρ1 and ρ2are legitimate states,so is their convex mixture. The set of separable states S is also compact and convex (seeFigure 1). From the theory of convex sets and Hahn-Banach theorem we conclude that for any entangled state there exists a hyperplane in the space of operators separating rhofrom S. Such a hyperplane defines uniquely a Hermitian operator W (observable) which has the following properties: The expectation value of W on all separable states, <W> ≥ 0, whereas its expectation value on ρ is negative, i.e. <W>ρ< 0.Figure 1Such an observable is for obvious reasons called entanglement witness, since it “detects” the entanglement of ρ. Every entangled state has its witnesses; the problem obviously is to find appropriate witnesses for a given state. To find out whether a given state is separable one should check whether its expectation value is non-negative for all witnesses. Obviously this is a necessary and sufficient separability criterion, but unfortunately it is not operational, in the sense that there is no simple procedure to test for all witnesses.Nevertheless, witnesses provide a very useful tool to study entanglement, especially if one has some knowledge about the state in question. They provide a sufficient entanglement condition, and may be obviously optimized (see Figure 2) by shifting the hyperplane in a parallel way towards S.Figure 2Bell inequalitiesAfter introducing the concept of separability and entanglement for mixed states, it is legitimate to ask what is the relation of mixed state entanglement and the existence of a LHV model, which requires that the state cannot violate any of the Bell-like inequalities. Let us discuss an example of such inequalities, the so called Clauser-Horne-Shimony- Holt inequality for two qubits. Let us assume that Alice and Bob measure two binary observables each, namely A 1, A 2, and B 1, B 2. The observables are random variables taking the values +1 or − 1, correlated possibly through some dependence on local hidden variables. It is easy to see that in the classical world, if B 1 + B 2 is zero, then B 1 − B 2 is either +2 or −2, and vice versa. Therefore if we define s = A 1(B 1 + B 2 ) + A 2 (B 1 − B 2 ) , we obtain that 2 ≥ s ≥ −2. This inequality holds also after averaging over various realizations. On the other hand, it can be shown that by taking suitable sets of observables for Alice and Bob we can find pure and even mixed quantum states that violate this inequality.Are Bell-like inequalities similar in this respect to witnesses, i.e. for a given entangled state can one always find a Bell-like inequality that “detects” it? The answer to this question is no, and has been already given by R. Werner in 1989. Even for two qubits there exist entangled states that admit an LHV model, i.e. cannot violate any Bell-like inequality.This observation indicates already that there is more structure in the “eggs” of Figure 1 and Figure 2. Separable states are evidently inside the PPT egg, according to the Peres condition. They admit an LHV model, i.e. they are also inside the LHV egg. But what about PPT entangled states? Do they violate some Bell-like inequality? Peres has formulated a conjecture that this not the case, and there is a lot of evidence that this conjecture is correct, although a rigorous proof is still missing.The distillability problem and bound entanglement Above we have classified quantum states according to the property of being either separable or entangled. An alternative classification approach is based on the possibility of distilling the entanglement of a given state. In a distillation protocol the entanglement of a given state is increased by performing local operations and classical communication on a set of identically prepared copies. In this way one obtains fewer, but “more entangled”, copies. This kind of technique was originally proposed in 1996 by Bennett and coworkers in the context of quantum teleportation, in order to achieve faithful transmission of quantum states over noisy channels. It also has applications in quantum cryptography as a method for quantum privacy amplification in entanglement based protocols in the presence of noise, as pointed out by David Deutsch and coworkers from Oxford.The distillability problem poses the question whether a given quantum state can be distilled or not. A separable state can never be distilled because the average entanglement of a set of states cannot be increased by local operations. Furthermore, the positivity of the partial transpose ensures that no distillation is possible. Thus, a given PPT entangled state is not distillable, and is therefore called bound entangled. There mayeven exist undistillable entangled states which do not have the PPT property. However, this conjecture is not proved at the moment.The first example of a PPT entangled state has been found by Pawel Horodecki from Gdansk in 1997. These states are so called edge states, which means that they cannot be written as a mixture of a separable state and a PPT entangled state. Particularly simple families of states have been suggested by Charles Bennett and coworkers at IBM, New York. They have found the so called unextendible product bases (UPB), i.e. sets of orthogonal product state-vectors, with the property that the space orthogonal to this set does not contain any product vector. It turns out that the projector onto this space is a PPT state, which obviously has to be entangled since it does not contain any product vector in its range (note that all state-vectors in the decomposition of a separable state ρinto a mixture of product states belong automatically to the range of ρ).The existence of bound entanglement is a mysterious invention of Nature. It is an interesting question to ask whether bound entanglement is a useful resource to perform quantum information processing tasks. It was shown so far that this is not the case for communication protocols such as quantum teleportation and quantum dense coding (i.e.a protocol that allows to enhance the transmission of classical information, using entanglement). However, surprisingly, it is possible to distill a secret key in quantum cryptography, starting from certain bound entangled states.Entanglement detectionAs discussed above, entanglement is a precious resource in quantum information processing. Typically in a real world experiment noise is always present and it leads to a decrease of entanglement in general. Thus, it is of fundamental interest for experimental applications to be able to test the entanglement properties of the generated states. A traditional method to this aim is represented by the Bell inequalities, a violation of which indicates the presence of entanglement. However, as mentioned above, not every entangled state violates a Bell inequality. So, not all entangled states can be detected by using this method.Another possibility is to perform complete state tomography, which allows determining all the elements of the density matrix. This is a useful method to get a complete knowledge of the density operator of a quantum system, but to detect entanglement it is an expensive process as it requires an unnecessary large number of measurements. If one has certain knowledge about the state the most appropriate technique is the measurement of the witness observable, which can be achieved by few local measurements. A negative expectation value clearly indicates the presence of entanglement.All these methods have been successfully implemented in various experiments. Recently another method for the detection of entanglement was suggested based on the physical approximation of the partial transpose. It remains a challenge to implement this idea in the laboratory because it requires the implementation of non local measurements.Entanglement measuresWhen classifying a quantum state as being entangled, a natural question is to quantify the amount of entanglement it contains. For pure quantum states there exists a well defined entanglement measure, namely the von Neumann entropy of the density operator of a subsystem of the composite state. For mixed states the situation is more complicated. There are several different possibilities to define an entanglement measure. The so called entanglement cost describes the amount of entanglement one needs in order to generate a given state. An alternative measure is the entanglement of formation, which is a more abstract definition. A further possibility to quantify entanglement is given by the minimum distance to separable states. Finally, motivated by physical applications, one can introduce the distillable entanglement which quantifies the extractable amount of entanglement.Unfortunately all of these quantities are very difficult to compute in general. For example, in order to determine the entanglement of formation one has to find the decomposition of the state that leads to the minimum average von Neumann entropy of a subsystem and this is a very challenging task. So far a complete analytical formula for the entanglement of formation only exists for composite systems of two qubits.Entanglement in multipartite systemsSo far, we have restricted ourselves to the case of composite systems with two subsystems, so called bipartite systems. When considering more than two parties, i.e multipartite systems, the situation becomes much more complex. For example, for the most simple tripartite case of three qubits, a pure state can be either completely separable, or biseparable (i.e. one of the three parties is not entangled with the other two), or genuinely entangled among all three parties. The latter class again consists of inequivalent subclasses, the so called GHZ and W states. This concept can be generalized to mixed states. For more than three parties it is easy to imagine that the number of subclasses grows fast.In recent years there has been much progress in the creation of multipartite entangled states in the laboratory. The existence of genuine multipartite entanglement has also been demonstrated experimentally by using the concept of witness operators.Even if the full classification of multipartite entanglement is a formidable task, certain classes of states, the so called graph states, have been completely characterized and shown to be useful both for quantum computational and quantum error correction protocols. Moreover, a deeper understanding of entanglement has proved to be very fruitful in connection with statistical properties of physical systems. All of these problems are discussed in more details in other sections of this publication.References[1] Einstein, P. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935)[2] J.S. Bell, Physics 1, 195 (1964)[3] P. Horodecki, Phys. Lett. A 232, 333 (1997)[4] M. Lewenstein et al., J. Mod. Opt. 47, 2481 (2000)[5] A. Peres, Phys. Rev. Lett. 77, 1413 (1996)[6] E. Schrödinger, Naturwissenschaften 23, 807 (1935)[7] R.F. Werner, Phys. Rev. A 40, 4277 (1989) Contact information of the author of this article Maciej LewensteinInstitut de Ciènces Fotòniques (ICFO)C/Jordi Girona 29, Nexus 2908034 BarcelonaSpainEmail: maciej.lewenstein@icfo.esChiara MacchiavelloIstituto Nazionale di Fisicadella Materia, Unita' di Pavia Dipartimento di Fisica "A. Volta"via Bassi 6I-27100 PaviaItalyEmail: chiara@unipv.itProf. Dr. Dagmar BrussInst. fuer Theoretische Physik IIIHeinrich-Heine-Universitaet Duesseldorf Universitaetsstr. 1, Geb. 25.32D-40225 Duesseldorf,GermanyEmail: bruss@thphy.uni-duesseldorf.de。
南京大学《量子化学》 (5)
9
(1) The electrons in a molecule move in the field of fixed nuclei. Thus, the kinetic energy of the nuclei can be neglected and the internuclear repulsion can be considered to be constant.
Physical quantity Conversion factor X
Length Mass Charge Energy
Angular momentum
a 0
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e
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Value of X (in SI)
5.2918 1011 m 9.1095 1031 kg 1.6022 1019 C 4.3598 1018 J
A1 B A
A1
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A
11
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rotation, and translation of a molecule is: H E with
nucl nucl
nucl
M
E R z z H nucl 2M R A1
1
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2
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{ elec
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A1 B A
AB AB
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1
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which provides a potential for nuclear motion.
《结构化学》教学大纲(英文版)
‘Structural Chemistry ’Course SyllabusCourse Code：09040001Course Category：Major BasicMajors：ChemistrySemester：SpringTotal Hours：54 Hours Credit：3Lecture Hours：54 HoursTextbooks：《Structural Chemistry》孙墨珑编著，东北林业大学出版社。
I.Introduction to Structural ChemistryThe major targets this course includes the followings: (1) to introduce the material structure of the basic concepts, basic theory, and basic methods for learning “Structural Chemistry”; (2) to explore the relationship between the microstructures and properties of atoms, molecules, and crystals; (3) to systematically clarify the essence of the periodic law of elements; (4) to deeply and qualitatively clarify the essence of the chemical bonds. This course introduces the basic principles of quantum mechanics and their applications in simple systems, structure of atoms, molecules, and crystals, symmetry of molecular orbitals, molecular orbital theory, and ligand field theory, etc. After learning this course, the students should be able to analyze and solve the basic chemistry problems from the point of view of quantum mechanics.II.Table of contentsSection I (Chapter 1) Basic knowledge of quantum mechanics1.1 Failures of classical mechanics1）Black-body radiation & Planck’s solution;2）Ph otoelectric effect & Einstein’s theory;3）Hydrogen spectrum & Bohr’s model.1.2Characteristics of the motion of microscopic particles1)Wave-particle duality;2)Uncertainty principle.1.3The basic postulates of quantum mechanics1)Postulate 1: wavefunction;2)Postulate 2: Hermitian operators;3)Postulate 3: Schrödinger equation;4)Postulate 4: linearity and superposition;5)Postulate 5: Pauli exclusion principle.1.4Applications of quantum mechanics in simple cases1)Free particle in one-dimensional (1D) box;2)Applications of the 1D-box model in simple chemical systems;3)Free particle in two-dimensional (2D) & three-dimensional (3D) box;4)Tunneling & scanning tunneling microscopy (STM).Section II (Chapter 2) Structures and properties of atoms2.1 One-electron atom: H atom1)The Schrödinger equation of H atoms;2)Solution of the Schrödinger equation of H atom.2.2Quantum numbers1)Principle quantum number, n;2)Angular momentum quantum number, l;3)Magnetic quantum number, m;4)Zeeman effect.2.3Wavefunction and electron cloud1)Radial distribution;2)Angular distribution;3)Spatial distribution.2.4 Structure of multi-electron atoms1)The Schrödinger equation of multi-electron atoms•Self-consistent field method;•Central field approximation.2)The building-up principles and electron configuration of multi-electron atoms•Pauli exclusion principle;•Principle of minimum energy;Hund’s rule.2.5Electron spin and Pauli exclusion principle2.6Atomic spectroscopy1)Orbital-spin coupling;2)Spectroscopic terms & term symbol;3)Derivation of atomic term.4)Hund’s rule on the spectroscopic terms;2.7Atomic properties1)Energy of ionization;2)Electron affinity;3)Electronegativity.Section III (Chapters 3-6) Structures and properties of molecules Chapter 3 Geometric structure of molecules─Molecular symmetry & symmetry point group3.1Symmetry elements and symmetry operations1)Symmetry elements and symmetry operations;2)Combination rules of symmetry elements;3.2Point groups & symmetry classification of molecules3.3Point groups & groups multiplication3.4Applications of molecular symmetry1)Chirality & optical activity;2)Polarity & dipole moment.Chapter 4 S tructure of biatomic molecules (X2 & XY)4.1 Linear variation method and structure of H2+ ion1) Shrödinger equation of H2+ ion;2) Linear variation method;3) Treatment of H2+ ion using linear variation method;4) Solutions of H2+ ion.4.2 Molecular orbital theory and diatomic molecules1) Molecular orbital theory;2) Structure of homonuclear diatomic molecules (X2);3) Structure of heteronuclear diatomic molecules (XY).4.3 Valence bond (VB) theory and H2 moleculeChapter 5 Structure of polyatomic molecules (A)5.1 Structure of Methane (CH4)1) Delocalized molecular orbitals of methane (CH4);2) Localized molecular orbitals of methane (CH4).5.2 Molecular orbital hybridization1) Theory of molecular orbital hybridization;2) Construction of hybrid orbitals;3) Structure of AB n molecules;4) Molecular stereochemistry: valence shell electron-pair repulsion (VSEPR)model.5.3 Delocalized molecular orbital theory─Hückel molecular orbital (HMO) theory1) HMO method & conjugated systems;2) HMO treatment for butadiene;3) HMO treatment for cyclic conjugated polyene (C n H n);4) Molecular diagrams;5) Delocalized π bonds.5.4 Structure of electron deficient molecules5.5 Symmetry of molecular orbitals and symmetry rules for molecular reactions5.6 Molecular spectroscopy1)Infrared absorption spectroscopy: molecular vibrations;2)Raman scattering spectroscopy: molecular vibrations;3)Fluorescence spectroscopy: electronic transitions;4)NMR spectroscopy: nuclear magnetic resonances.Chapter 6 Structure of polyatomic molecules (B), coordination compounds 6.1 Crystal field theory6.2 CO and N2 coordination complexes6.3 Organic metal complexes1) Zeise’s salts;2) Sandwich complexes.6.4 Clusters1) Transition-metal cluster compounds2) Carbon clusters and nanotubesSection IV (Chapters 7-9) Structure of crystalsChapter 7 Basics of crystallography7.1 Periodicity and lattices of crystal structure1) Characteristics of crystal structure;2) Lattices and unit cells;3) Bravais lattices and unit cells of crystals;4) Real crystals & crystal defects.7.2 Symmetry in crystal structure1) Symmetry elements and symmetry operations;2) Point groups (32) and space groups (230).7.3 X-Ray diffraction of crystals1) X-ray diffraction of crystals•Laue equation;•Bragg’s law;•Reciprocal lattice.2) Instrumentation of X-ray diffraction;3) Applications of X-Ray diffraction•Single crystal diffraction: crystal structure determination;•Powder diffraction: qualitative & quantitative analysis of crystalline materialsChapter 8 Crystalline solids, I: metals and alloys8.1 Close Packing of Spheres1) Close packing of identical spheres;2) Packing density;3) Interstices.8.2 Structures and Properties of Pure Metals8.3 Structures and Properties of AlloyChapter 9 Crystalline solids, II: ionic crystals9.1 Packing of Ions;9.2 Crystal Structure of Some Typical Ionic Compounds9.3 Trend of Variation of Ionic Radii9.4 Pauling Rule of Ionic Crystal Structure9.5 Crystals of Functional Materials1) Nonlinear optical materials;2) Magnetic materials;3) Conductive polymers;4) Semiconductors: band gap and photocatalysisIII.Table of ScheduleReferences[1] 王荣顺主编，东北师范大学等，《结构化学》，高等教育出版社，2003年。
操作系统-精髓与设计原理 WILLIAM STALLINGS 课后答案
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TABLE OF CONTENTS Chapter 1 Computer System Overview...............................................................4 Chapter 2 Operating System Overview...............................................................7 Chapter 3 Process Description and Control........................................................8 Chapter 5 Concurrency: Mutual Exclusion and Synchronization .................10 Chapter 6 Concurrency: Deadlock and Starvation ..........................................17 Chapter 7 Memory Management .......................................................................20 Chapter 8 Virtual Memory ..................................................................................22 Chapter 9 Uniprocessor Scheduling...................................................................28 Chapter 11 I/O Management and Disk Scheduling ........................................32 Chapter 12 File Management ..............................................................................34
半导体双语专业常见单词
Chapter 2Quantum['kwɔntəm] Mechanics[mɪ'kænɪks]量子力学accuracy['ækjurəsi]n. 精确(性), 准确(性)theoretical [,θiə'retikəl]adj. 理论的；推想的, 假设的electromagnetic wave [ɪ,lektrəʊmæg'netɪk]电磁波inconsistent[,ɪnkən'sɪstənt]adj. (思想、意见等)不一致的, 不协调的；易变的, 不稳定的, 反复无常的Energy Quanta 能量子，量子Relativity 相对论The blackbody radiation (黑体辐射)particle (粒子)unambiguous[,ʌnæm'biɡjuəs]adj. 不含糊的; 清楚的; 明确的thermal ['θə:məl] radiation热辐射photoelectric[,fəʊtəʊɪ'lektrɪk] effect （光电效应）.electrodes [ɪ'lek,trəʊd]n. 电极irradiate [i/reidieit] (照射)incident light （入射光）threshold ['θreʃhəuld[ frequency 截止频率proportional to [prə'pɔ:ʃənəl]adj. 比例的, 成比例的Photoelectric[,fəʊtəʊɪ'lektrɪk]adj. 光电的intensity [in'tensiti]n. 强烈, 剧烈；(感情的)强烈程度photoelectron[,fəutəui'lektrɔn]n. 光电子kinetic [kɪ'netɪk, kaɪ-]adj. <物>动力的,由运动引起的electrode [ɪ'lek,trəʊd]n. 电极emission[ɪ'mɪʃən] n.1．排放物,散发物(尤指气体)2．排放,散发,发出(气体、光、热)eject[i'dʒekt]vt. & vi. 弹出, 喷出, 排出vt. 逐出contamination (污染)hypothesis [hai'pɔθisis]n. 假说, 假设, 前提assumption [ə'sʌmpʃən]n. 假定, 臆断photon [/fəʊ:tɔn]光子;光量子cathode['kæθ,əʊd]n. <电>(-)阴极,负极work function (功函数).equation方程kinetic energy （动能）photon. ['fəʊ,tɔn]n. <物>光子;光量子photoelectron [,fəutəui'lektrɔn]n. 光电子reciprocal ri'siprəkəl (倒数)Wave-Particle Duality [dju(:)'æliti] (波粒二象性)impinges [im/pindʒ] (冲击,撞击)diffuse reflection漫射wavelength 波长scattere.[/skætə]散射mechanism ['mekənizəm]n. (机理)forced vibration [vaɪ'breɪʃən] (受迫振动),oscillate vt. & vi. (使)摆动momentum（动量）collision [kə'liʒən]n. 碰撞, 冲突, 抵触recoils [ri/kɔil] 反冲D e B r o g l i e W a v e(德布罗意波)postulate [/pɔstju/leɪt] (假设matter waves 物质波wave-particle duality [dju(:)'æliti](波粒二象性)filament['fɪləmənt (灯丝)accelerate [æk'seləreit]vt. & vi. (使)加快, (使)增速nickel ['nikəl] (镍).Scattere [/skætə]散射diffract 衍射interference [,ɪntə'fiərəns]干涉grating ['greɪtɪŋ]（光栅）magnitude 'mæɡnitju:d] (数量级)protons [/prəʊ/tɔn] (质子)neutrons [/nu:/trɔn] (中子)mechanics [mɪ'kænɪks]n. 力学;机械学；机件;过程;方法radius ['reidjəs (半径)wave theory 波动理论subatomic ['sʌbə'tɔmik]adj. 小于原子的;亚原子的,次原子的particle ['pɑ:tikl]n. 微粒, 颗粒, 〈物〉粒子；极少量；小品词conjugate [/kɔndʒəɡeit]variables [/vɛəriəbl](相关变量), simultaneous [,siməl'teinjəs]adj. 同时发生的; 同时存在的generalized[/dʒenərəlaizd]adj.1．广泛的, 普遍的, 全面的2．非具体的; 整体的angular position (角坐标)angular momentum (角动量momentum [məu'mentəm]n. 动力, 冲力, 势头；〈物〉动量profound [prə'faund]adj. 深度的; 深切的; 深远的；知识渊博的, 见解深刻的, 深奥的diameter [dai'æmitə]n. 直径；放大率electron single-slit diffraction（[di'frækʃən]电子单缝衍射slit [slit]vt. 切开, 撕开n. 狭长的口子, 裂缝billiard [/bɪljəd] ball (台球)macroscopic [/mækrə/skɔpɪk] (宏观的)Microscopic [/maɪkrə/skɔpɪk] 微观的rifle [/raifl] (来福枪)bullet [/bulit] (子弹)apparatus [/æpə/reitəs] (仪器)bounced off 反弹probability density function (概率密度函数)precisely [prɪ'saɪsli:]adv. 精确地;恰好;细心地；对, 的确如此dice [dais]骰子violate ['vaiəleit]vt. 违反, 违背；亵渎；侵犯, 妨碍bizarre [bi/zɑ:] (怪诞的tick [tik]n. 钟的嘀嗒声；(表示正确无误的)记号；证券价格的增额；(寄生于体大动物的吸血小虫)壁虱vt. & vi.1．发出滴答声2．标以记号3．激怒kinetic energy 动能relativistic quantum mechanics (相对论量子力学non-relativistic quantum mechanics (非相对论量子力学) . hypotheses [hai/pɔθisiz]臆测,假定one-dimensional (一维的),constant ['kɔnstənt] (常数)portion ['pɔ:ʃən]n. 一部分, 一份vt. 把…分成份额, 分配the technique of separation of variables (分离变量法Substituting ['sʌbstitju:tiŋ]n. 取代denote [di'nəut]vt. 为…的符号; 为…的名称；指示; 指出dynamic [dai'næmik] (动力学的complex conjugate function (复共轭)normalizing condition 归一化条件coefficient [,kəʊə'fɪʃənt系数).derivative [di/rivətiv](导数)finite ['fainait]adj. 有限的, 有限度的；〈语〉限定的single-valued 单值的state superposition principle (态叠加原理)traveling wave (行波),parameter [pə'ræmitə]n. (限定性的)因素, 特性, 界限；〈物〉〈数〉参量, 参数Infinite ['infinit]adj. 无限的, 无穷的, 无边无际的Potential Well (势阱)bound particle (束缚粒子).explicit [iks'plisit]adj. 详述的, 明确的, 明晰的；直言的, 毫不隐瞒的, 露骨的discrete [dis'kri:t]adj. 分离的, 不相关联的energy levels （能级）dimension [di'menʃən]n. 尺寸, 维度standing wave (驻波quantization量子化quantum states (量子态)Barrier ['bæriə] (势垒)incident particle (入射粒子)a flux （[flʌks]of incident particles一束入射离子流originate [ə'ridʒineit]vi. 起源于, 来自, 产生transmission coefficient (透射系数),impinge [im/pindʒ]碰撞penetrate ['penitreit] (穿透)tunneling (tunnel [/tʌnəl]) effect (隧道效应contradict [,kɔntrə'dikt]vt. & vi. 反驳, 否认…的真实性vt. 与…发生矛盾, 与…抵触tunnel diode （隧道二级管）horizontal [,hɔri'zɔntəl]adj. 水平的, 与地平线平行的ionize ['aɪə,naɪz]vt. & vi. (使)电离,(使)成离子molecule分力theoretical [,θiə'retikəl]adj. 理论的；推想的, 假设的visualized ['viʒuəlaiz]vt. 在脑中使(某人或某物)形象化, 设想, 想像pulse [pʌls]n. 脉搏；脉冲vi. (心脏)跳动; 脉动attosecond阿秒periphery [pə'rɪfəri:]n. 外围;边缘spectrometry光谱测定法dynamics [dai'næmiks]n. 动力学、力学；facilitate [fə'siliteit]vt. 使便利, 减轻…的困难rectangular [rek/tæŋɡjulə](长方形的; 矩形的coulomb [/ku:lɔm]attraction (库仑引力)permittivity [/pə:mi/tiviti] (介電常數)spherical coordinates [/sfɪərɪkəl] [kəu/ɔ:dineit] (球坐标). Laplace operator (拉普拉斯算符)spherical['sfɪərɪkəl, 'sfer-]adj. 球形的,球面的；天体的coordinate[kəu'ɔ:dineit]vt. 使协调; 使调和adj. 同等的, 并列的n. 〈数〉坐标principle quantum number (主量子数);angular momentum quantum number (角量子数magnetic quantum number (磁量子数).Correspond[,kɔris'pɔnd]vi. 相符合, 相一致；相当, 相类似；通信discrete[dis'kri:t]adj. 分离的, 不相关联的，分立的symmetric对称的Bohr radius (玻尔半径emanate ['emə,neɪt]vi. 从…处传出;传出nucleus ['nju:kliəs]n. (原子)核；中心, 核心plot 绘制，作图electron cloud (电子云energy shell能量壳层yield [ji:ld]vt. & vi. 生产, 出产, 带来；evolve [i'vɔlv]vt. & vi. 演变; 进化Periodic （[,piəri'ɔdik]）T able (周期表) initial [i'niʃəl]adj. 最初的, 开头的electron spin (电子自旋).spin [spin]vt. & vi. 使…旋转vt. 杜撰exclusion [ɪk'sklu:ʒən]n. 拒绝,排除n. 排外主义helium (氦),inert [ɪ/nɜ:t](惰性的valence ['veiləns]n. (化合)价,原子价deviate [/di:vieit] (偏离)。
量子力学英文读物
量子力学英文读物以下是一些关于量子力学的英文读物推荐：1. "Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality" by Manjit Kumar2. "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" by Brian Greene3. "The Quantum World: Quantum Physics for Everyone" by Kenneth W. Ford4. "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili5. "Quantum Physics: A Beginner's Guide" by Alastair Rae6. "Quantum Computing for Computer Scientists" by Noson S. Yanofsky and Mirco A. Mannucci7. "Quantum Physics for Babies" by Chris Ferrie (a simplified introduction for children and adults)8. "The Strange World of Quantum Mechanics" by Daniel F. Styer这些书籍从不同的角度介绍了量子力学的基本原理、应用、历史以及相关的思想争论。
根据你的兴趣和程度，选择适合你的读物开始探索量子世界吧！。
绪论讲稿
Chapter 0 Introduction （绪论）120世纪物理学取得的两个划时代的进展是相对论和量子力学。
相对论的建立，从根本上改变了人们原有的时空观，并指明了牛顿力学的适用范围。
量子力学的建立，开辟了人们认识微观世界的道路。
原子和分子之谜被揭开了。
物质的属性以及在原子水平上的物质结构这个古老而又基本的问题才原则上得以解决（例如，物体为何有导体、半导体和绝缘体之分？为何有顺磁体、反磁体和铁磁体之分？等）。
在量子力学中人们找到了化学和物理学的紧密联系（搞清楚了原子周期律和分子键的本质）。
大量事实证明，离开了量子力学，任何一门近代物理学科及相关的边缘学科的发展都是不可思议的。
可以毫不夸张地说，没有量子力学的建立，就没有人类的现代物质文明。
2·Unlike Newton's mechanics, or Maxwell's electrodynamics, or Einstein's relativity, quantum theory was not created—or even definitively packaged—by one individual. （Preface, ix）(与牛顿力学、麦克斯韦电动力学、爱因斯坦广义相对论不同。
量子理论不是由单个人创立，或集大成。
)Planck (1900), Einstein (1905), Bohr (1912)de Broglie (1923), Heisenberg (1925), Schrodinger (1926), Born (1926), Dirac (1927)“量子英雄”3·If you are not confused by quantum mechanics then you haven’t really understood quantum mechanics. —N. Bohr（如果你没有被量子力学搞糊涂的话，那么你还没有真正理解量子力学。
量子力学英文课件格里菲斯chapter0
1925—1927年是物理学急剧变革的年代！
1925年：7月海森伯发表创建量子力学的第一篇论文 9月玻恩、约当认识到需要一种矩阵力学 11月玻恩、约当、海森伯给出矩阵力学 11月狄拉克提出量子代数 1926年：1月薛定谔发表第一篇波动力学论文 7月玻恩发表第一篇量子力学统计解释论文 8月狄拉克提出波函数与粒子统计性质的关系 1927年：3月海森伯测不准关系提出 5月泡利矩阵提出 9月玻尔提出互补原理
Part I Theory
Chap.1 The Wave Function Chap.2 The Time-Independent Schrodinger Equation Chap.3 Formalism Chap.4 Quantum Mechanics in Three Dimensions Chap.5 Identical Particles
(但我们所“做”的和我们所讲的这些故事，就像“舍赫拉查德的传说”一样变化多端， 令人难以置信)
Tales of Scheherazade
Queen Scheherazade (舍赫拉查德 ) tells her stories to King Shahryar (山鲁亚尔 ) !
One Thousand and One Nights
Why should we study the Quantum Mechanics ? What is the Quantum Mechanics ? How to study Quantum Mechanics ?
实验
Comparison of Rayleigh-Jeans law with Wien's law and Planck's law, for a body of 8 mK temperature. /wiki/Rayleigh-Jeans_law
物理学类专业英语_基础课程
Introduction 1 参考译文：导论 3Chapter 1: Mechanics 61.1 Classical versus quantum 61.2 Einsteinian versus Newtonian 61.3 History 71.4 Types of mechanical bodies 81.5 Sub-disciplines in mechanics 81.5.1 Classical mechanics 81.5.2 Quantum mechanics 9参考译文：第一章力学 91.1 经典和量子 91.2 爱因斯坦和牛顿 101.3力学的历史 101.4力学中物体的种类 111.5力学的分支学科 111.5.1经典力学有如下学科构成： 111.5.2量子力学 12Chapter 2: Heat 132.1 Overview 132.2 Notation 142.3 Definitions 152.4 Thermodynamics 152.4.1 Internal energy 152.4.2 Heat capacity 162.4.3 Phase Changes 172.5 Heat transfer mechanisms 17 2.6 Heat dissipation 19参考译文：第二章热学 202.1 综述 202.2 符号 212.3 定义 212.4 热力学 212.4.1 内能 212.4.2 热容量 222.4.3 相变 232.5 热传递的机制 232.6 散热 24Chapter 3: Electromagnetism 25 3.1 History 253.2 Overview 273.3 Classical electrodynamics 27 3.4 The photoelectric effect 28 3.5 Maxwell's equations 293.6 Special relativity 30参考译文：第三章电磁学 343.1 发展历史 353.2 总论 363.3 经典电动力学 363.4 光电效应 373.5 麦克斯韦方程组 373.6 狭义相对论 37Chapter 4 Optics 414.1 History 414.2 Classical optics 434.2.1 Geometrical optics 44 4.2.2 Physical optics 46 4.3 Modern optics 514.3.1 Lasers 524.3.2 Nonlinear optics 59 参考译文：第四章光学 59 4.1 光学的历史 604.2 经典光学 614.2.1 几何光学 614.2.2 物理光学 634.3 现代光学 664.3.1激光 664.3.2 非线性光学 71Chapter 5 Atomic physics 725.1 Isolated atoms 725.2 Electronic configuration 725.3 History and developments 735.3.1 Introduction to Atomic Physics 74 5.3.2 Atomic Structure 745.3.3 Bohr atom structure model 755.3.4 Atomic Isotopes 765.3.5 Einstein's Equation 765.3.6 Radioactive Decay 77参考译文：第五章原子物理 795.1 孤立原子 795.2 电子图像 795.3 原子物理的历史和发展过程 805.3.1 原子物理引论 805.3.2 原子结构 805.3.3波尔的原子结构模型 815.3.4 原子的同位素 815.3.5 爱因斯坦方程 825.3.6 放射性衰变 82Chapter 6: Quantum mechanics 846.1 Overview 856.2 Quantum mechanics and classical physics 86 6.3 Theory 866.4 Mathematical formulation 89。
griffiths d.j.introduction to quantum mechanics..s
25 25 − 21 = 4
σ2 = 1 N
(∆j)2N (j) = 1 (−7)2 + (−6)2 + (−5)2 · 3 + (1)2 · 2 + (3)2 · 2 + (4)2 · 5 14
= 1 (49 + 36 + 75 + 2 + 18 + 80) = 260 = 18.571.
14
14
CHAPTER 1. THE WAVE FUNCTION
3
Chapter 1
The Wave Function
Problem 1.1
(a) j 2 = 212 = 441.
j2 = 1 N
j2N (j) = 1 (142) + (152) + 3(162) + 2(222) + 2(242) + 5(252) 14
4
CHAPTER 1. THE WAVE FUNCTION
Problem 1.2
(a)
x2 =
h
x2
√1
dx =
√1
2 x5/2
h h2 =.
0 2 hx
2h 5
05
σ2 = x2 − x 2 = h2 −
Contents
Preface
2
1 The Wave Function
3
2 Time-Independent Schrödinger Equation
14
3 Formalism
62
4 Quantum Mechanics in Three Dimensions
87
5 Identical Particles
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英文原版量子论科普
英文原版量子论科普全文共四篇示例，供读者参考第一篇示例：One of the key principles of quantum mechanics is the concept of superposition. This principle states that particles can exist in multiple states at the same time. For example, an electron can be in a state of both spin up and spin down simultaneously. This is in contrast to classical mechanics, where particles are assumed to have definite positions and properties at all times.第二篇示例：The development of quantum mechanics began in the early 20th century with the work of physicists such as Max Planck, Albert Einstein, and Niels Bohr. One of the key insights of quantum mechanics is that particles such as electrons and photons can exhibit both particle-like and wave-like behavior. This wave-particle duality is a central feature of quantum mechanics and has important implications for the behavior of particles at the quantum level.第三篇示例：Quantum mechanics, also known as quantum physics or quantum theory, is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales of atoms and subatomic particles. It is a branch of physics that deals with the behavior of matter and energy on the scale of atomic and subatomic particles.第四篇示例：Quantum mechanics, a branch of physics that involves the study of the behavior of particles at the smallest scales, has often been described as one of the most mysterious and counterintuitive theories in science. This is because it challenges our classical understanding of the physical world, introducing concepts such as superposition, entanglement, andwave-particle duality.。
lecture8
quantum mechanics
Not the mathematics, but the interpretation!
Quantum Mechanics
Quantum mechanics vs. classical mechanics
Classical mechanics Quantum mechanics particle abstraction wave particle duality
Quantum Physics
Two founders of QM among many others
The Nobel Prize in physics 1933
for the discovery of new productive forms of atomic theory
E. Schrö dinger P.A.M. Dirac 1887-1961 1902-1984 Austria United Kingdom
Quantum Mechanics
Probability amplitude and probability density
wave function
complex conjugate
positive and real
Quantum Mechanics
Normalization
The integral of over all space must be finite if is to describe properly a real body.
Quantum Mechanics
Wave functions add, not probabilities
5.4 Linearityinger equation is linear in the wave function . As a result, a linear combination of solutions of Schrö dinger equation for a given system is also itself a solution. Superposition principle Thus we conclude that the interference effects can occur for wave functions just as they can for light, sound, water, and electromagnetic waves.
SAT 化学词汇表
（12g12C 含有的原子数，约为 6.02×1023） Group Ⅲ- 第三族
azide 叠氮化物
Group Ⅳ-Carbonic Group 碳族
balance chemical equation 配平化学方程 Group Ⅴ-Nitric Group 氮族
式
Group Ⅵ-Oxygenic Group 氧族
物里各物质都保持原来的性质）
浓度）
molar mass 摩尔质量（1 摩尔物质的质量） vaporize 汽化
molarity 摩尔浓度，也叫物质的量浓度（以 vertical axis 纵坐标
1 升即 1 立方分米溶液里含有多少摩溶质来 vice versa 反之亦然
表示溶液组成的物理量）
volume 体积
tritium 氚
dioxide 二氧化物
X-ray X 射线
dissolve 溶解
α-particles α 粒子，即 alpha-particle（带 dropwise 逐滴地 有两个质子和中子的粒子，即氦原子核，对 electric current 电流
物质的穿透力较强，流速约为光速的 1/10） empirical formulae 实验式，经验式（只表
Chapter 2 abbreviation 缩写 absorption 吸收 abundance 丰度 accelerate 加速
equation 方程式 ethanoic acid 乙酸 filament 灯丝 formula （pl. formulae） 化学式（用元素 符号来表示物质组成的式子）
SAT II 化学词汇表
ห้องสมุดไป่ตู้
Part 1 foundation chemistry 基础化学
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量子力学与统计物理（Quantum mechanics and Statistical Physics）黄建明电子工程学院北京邮电大学，北京100876北京邮电大学北京1008761J. –M. Huang目录第章量子力学的诞生第一章第二章波函数和Schrodinger 方程第三章一维定态问题第四章量子力学中的力学量第五章态和力学量表象第六章近似方法第七章量子跃迁第八章自旋与全同粒子2J. –M. Huang第五章态和力学量表象§1 态的表象§2 算符的矩阵表示2§3 量子力学公式的矩阵表述§4 Dirac 符号§5 Hellmann –Feynman 定理及应用§6 占有数表象§7 么正变换矩阵73J. –M. Huang1§1 态的表象到目前为止，体系的状态都用坐标(x, y, z)的函数表示，也就是说描写状态的波函数是坐标的函数。
力学量则用作用于坐标函数的算符表示。
但是这种描述方式在量子力学中并不是唯一的，这正如几何学中选用坐标系不是唯一的一样。
坐标系有直角坐标系、球坐标系、柱坐标系等，但它们对空间的描写是完全是等价的。
波函数也可以选用其它变量的函数，力学量则相应的表示为作用于这种函数上的算符。
表象：量子力学中态和力学量的具体表示方式称为表象。
以前采用的是坐标表象，下面我们要介绍其他表象。
（一）动量表象（二）力学量表象（三）讨论4J. –M. Huangddx t x x t p C p ),()(*),(Ψ=∫ψdpt p C t p C ),(*),(∫=5J. –M. HuangC (p , t ) 物理意义|Ψ(x,t)|2d x是在Ψ(x,t)所描写的状态中，测量粒子的位置所得结果在|C(p,t)|2d p (t)所描写的状态中测量粒子的动量所得结果在x → x + d x 范围内的几率。
是在Ψ(x,t)所描写的状态中，测量粒子的动量所得结果在p → p + d p 范围内的几率。
Ψ(x,t)与C(p,t)一一对应，描述同一状态。
Ψ(x,t)是该状态在坐标表象中的波函数；而C(p,t)就是该状态在动量表象中的波函数。
6J. –M. Huangx −′′−′)()()()(x x x x x x x x x −′==′δψδδ所以7J. –M. Huang（二）力学量表象推广上述讨论：x, p都是力学量，分别对应有坐标表象和动量表象，因此可以对任何力学量Q都建立一种表象，称为力学量Q表象。
那末，在任一力学量Q表象中，问题Ψ(x,t)所描写的态又如何表示呢？（1）具有分立本征值的情况（）2）含有连续本征值情况J. –M. Huang（1）具有分立本征值的情况设算符Q 的本征值为：Q 1, Q 2, ..., Q n , ...，u 都是归化的相应本征函数为：u 1(x ), u 2(x ), ..., u n (x ), ...。
将(x,t)∑=Ψx u t a t x n n )()(),(若Ψ, u n 都是归一化的，则a n (t)也是归一化的。
Ψ(x,t) 按Q 的本征函数展开：∫Ψ=dxt x x u t a n n n).()(*)(证：dxx u t a x u t a n n nm m m)()(*)]()([∑∑∫=a 1(t),a 2(t),...,a n (t),...就是Ψ(x,t)所描写状态在Q 表象中的表示。
∫ΨΨ=dxt x t x ).(),(*1dx x u x u t a t a n m n m mn)()(*)()(*∫∑∑=*=由此可知，| | 2 表示mnn m mnt a t a δ)()(∑∑)()(*t a t a n n n∑=，|a n |表在Ψ(x,t)所描述的状态中测量Q 得Q n 的几率。
9J. –M. Huang写成⎟⎞⎜⎛)(1t a 共轭矩阵矩阵形式⎟⎟⎟⎜⎜⎜=Ψ )(2t a ()*)(*)(*)(21t a t a t a n =Ψ+⎟⎟⎠⎜⎜⎝ )(t a n ⎛归一化可写为)()(***21⎟⎟⎟⎞⎜⎜⎜+t a t a a ())()()()(21⎟⎟⎟⎜⎜⎜=ΨΨt a t a t a t n n1)(*)(==⎠⎝∑t a t a n n n10J. –M. Huang（2）含有连续本征值情况例如氢原子能量就是这样一种力学量，即有分立也有连续本征值。
设力学量Q 的本征值和本征函数分别为：Q 1, Q 2, ..., Q n , ..., q u 1(x), u 2(x), ..., u n (x), ..., u q (x)⎪⎩⎪⎨⎧Ψ=Ψ=∫∫dxt x x ut adx t x x u t a qqn n ),()(*)(),()(*)(则dqx u t a x u t a t x q q n n n)()()()(),(∫∑+=Ψ|a n (t)|2是在Ψ(x,t) 态中测量力学量归一化则变为：1)()(*)()(*=+∫∑dq t a t a t a t a q q n n nQ 所得结果为Q n的几率；|a 2dq (x t)⎞⎛)(1t a q (t)|dq 是在Ψ(x,t) 态中测量力学量Q 所得结果在q → q + dq 之间的几率。
在这样的表象中，Ψ 仍可以用个列矩阵⎟⎟⎟⎟⎜⎜⎜⎜=Ψ)(2t a 仍可以用一个列矩阵表示：⎟⎟⎟⎟⎠⎜⎜⎜⎜⎝)()(t a t a q n ()*)(*)(*)(*)(21t a t a t a t a q n=Ψ+归一化仍可表为：Ψ+Ψ= 111J. –M. Huang()()()i j ku1(x), u2(x),..., u n(x), ...i, j, k,a1(t), a2(t),..., a n(t), ... A x, A y, A z态矢量量子状态Ψ(x,t) 矢量A12J. –M. Huang所以可以把状态看成是一个矢量——Ψ看成是个矢量态矢量。
选取一个特定力学量Q 表象，相当于选取特定的坐标系，(x),u (x),...,u (x),...u 1(x), u 2(x), ..., u n (x), ... 是Q 表象的基本矢量简称基矢。
波函数⎟⎟⎞⎜⎜⎛)()(21t a t a 是态矢量Ψ在Q 表象中沿各基矢方向上的“分量”。
表象的基矢有无限多个，所⎟⎟⎟⎟⎜⎜⎜⎜=Ψ)(t a n 。
Q ，以态矢量所在的空间是一个无限维的抽象的函数空间，称为Hilbert 空间。
⎠⎝13J. –M. Huang§２算符的矩阵表示（一）力学量算符的矩阵表示（二）Q表象中力学量算符F的性质（三）Q有连续本征值的情况14J. –M. Huangdx x u i x F x u F m xn nm )(),(ˆ)(*∂∂−≡∫表达方式15J. –M. Huang⎟⎟⎟⎟⎜⎜⎜⎜⎟⎟⎟⎟⎜⎜⎜⎜=⎟⎟⎟⎟⎜⎜⎜⎜)()(21t a F F F t b m nm n n n Φ=F Ψ16J. –M. Huang⎠⎝⎠⎝⎠⎝(=(=(=0⎞⎛001单形式是个对角矩阵L x )11 = (L x )22 = (L x )33 = 0 (L x )13 = (L x )31 = 0(L x )12=(L x )21=(L x )23=(L x )32= /21/2⎟⎟⎟⎠⎜⎜⎜⎝−=100000z L 单形式，是一个对角矩阵，对角元素就是L z 的本征值。
17J. –M. Huang⎛0i ⎟⎟⎟⎠⎞⎜⎜⎜⎝−−=00002i i i yL =⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=000002i i i i 厄密矩阵18J. –M. Huang（2）力学量算符在自身表象中的形式)()(ˆx u Q x u Q nn n =结论：算符在自身表象中是一Q 的矩阵形式对角矩阵，对角元素就是算符的本征值。
ˆ*⎟⎞⎜⎛Q 01m n m mn nm dx x u x u Q dx x u Q x u Q ==∫∫)()(*)()(⎟⎟⎟⎜⎜⎜=Q Q 002nmm Q δ=⎟⎟⎠⎜⎜⎝n Q 0019J. –M. Huang∫只是该矩阵的行列是不是n可数的，而是用连续下标表示20J. –M. Huang)′′δ)()(p p i p ′−=∂∂δ (p p p −=dxx x i p p p )()(*)(′∂∂∫=ψψ 21J. –M. Huang§3 量子力学公式的矩阵表述（一）平均值公式（二）本征方程（三）Schrodinger方程的矩阵形式22J. –M. Huang=***t a t a t a F ()⎟⎟⎟⎠⎜⎜⎜⎝⎟⎟⎟⎠⎜⎜⎜⎝)()(,),(),(2121t a F F F n mn m m m ΨΨ=F F *23J. –M. Huang上式是一个齐次线性方程组210)(==−∑m a F n mnmn nλδ⎟⎠⎜⎝于是求解微分方程的问题就化成了求解代数方程根的问题。
24J. –M. Huang,,⎛⎛12⎛⎟⎟⎟⎠⎞⎜⎜⎜⎝=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛⎟⎟⎟⎠⎞⎜⎜⎜⎝321321*********a a a a a a λ 02022321=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎟⎟⎟⎟⎟⎟⎜⎜⎜⎜⎜⎜−−a a a λλ0222=−−λλ 解得本征值λ=0,± .25J. –M. Huang⎠⎝⎟⎜=⎟⎜=⎟⎜=−0⎟⎟⎠⎜⎜⎝−⎟⎟⎠⎜⎜⎝−⎟⎟⎠⎜⎜⎝21211211021211ξξξ26J. –M. Huang∂⎟⎟⎟⎟⎠⎜⎜⎜⎜⎝⎟⎟⎟⎟⎠⎜⎜⎜⎜⎝=⎟⎟⎟⎟⎠⎜⎜⎜⎜⎝∂)()(21t a H H H t a t i n m n m m n Ψ,H都是矩阵27J. –M. Huang4Dirac§4 Dirac 符号（一）引（二）态矢量（三）算符（四）总结28J. –M. Huang表象中的形式(一）引z 前四章给出的都是X -表象中的形式，z 本章中给出了任一力学量Q -表象中的形式，它们都是取定了某一具体的力学量空间即某一具体的力学量取定了某一具体的力学量空间，即某一具体的力学量表象。
量子描述除了使用具体表象外，也可以不取定表象，正如几何学和经典力学中也可用矢量形式A 来，表示一个矢量，z 而不用具体坐标系中的分量(A ,A ,A )表示一样。
x y z z 量子力学可以不涉及具体表象来讨论粒子的状态和运动规律。
这种抽象的描述方法是由Dirac 首先引用的，z 所以该方法所使用的符号称为Dirac 符号。
29J. –M. Huang(二)态矢量（1）右矢空间前面已经讲过，一个状态通过一组力学量完全集的测量（完全测量）来确定，通常用所测得的力学量的量子数来确定。