量子力学英文名词 ppt课件
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量子力学英文课件格里菲斯Charter10
In molecular physics, this technique is known as the Born-Oppenheimer （玻恩-奥本海默）approximation.
In quantum mechanics, the essential content of the adiabatic approximation can be cast in the form of a theorem.
Here we assume that the spectrum is discrete and nondegenerate throughout the transition from Hi to Hf , so there is no ambiguity（歧义） about the
ordering of the states; these conditions can be relaxed, given a suitable procedure for “tracking” （跟踪）the eigenfunctions, but we’re not going to pursue that
A case in point is our discussion of the hydrogen molecule ion.
We began by assuming that the nuclei were at rest, a fixed distance R apart, and we solved for the motion of the electron.
and they are complete, so the general solution to the time-dependent Schrödinger equation
量子力学英文课件格里菲斯Chapter6
Writing n and En as power series in , we have
Here : En1 is the first-order correction to the nth eigenvalue, n1 is the first-order correction to the nth eigenfunction; En2 and n2 are the second-order corrections, and so on.
To first order (1),
To second order (2),
and so on. We’re done with , now — it was just a device to keep track of the different orders — so crank it up to 1.
The right side is a known function, so this amounts to an inhomogeneous differential equation for n1. Now, the unperturbed wave functions constitute a complete set, so n1 (like any other function) can be expressed as a linear combination of them:
but unless we are very lucky, we’re unlikely to be able to solve the Schrö dinger equation exactly, for this more complicated potential. Perturbation theory is a systematic procedure for obtaining approximate solutions to the perturbed problem by building on the known exact solutions to the unperturbed case.
量子力学英文课件格里菲斯Charter8
It is particularly useful in calculating bound-state energies and tunneling rates through potential barriers.
The essential idea is as follows: Imagine a particle of energy E moving through a region where the potential V(x) is constant.
Suppose we have an infinite square well with a bumpy bottom (Figure 8.2):
Inside the well [assuming E > V(x) throughout] we have or, more conveniently, where
rather slowly in comparison to , so that over a region
containing many full wavelengths the potential is essentially constant.
Then it is reasonable to suppose that remains
F is the transmitted amplitude, and the tunneling probability is
In the tunneling region ( 0 x a ), the WKB approximation gives
But if the barrier is very high and/or very wide, then the coefficient of the exponentially increasing term (C) must be small, and the wave function looks something like Figure 8.4.
The essential idea is as follows: Imagine a particle of energy E moving through a region where the potential V(x) is constant.
Suppose we have an infinite square well with a bumpy bottom (Figure 8.2):
Inside the well [assuming E > V(x) throughout] we have or, more conveniently, where
rather slowly in comparison to , so that over a region
containing many full wavelengths the potential is essentially constant.
Then it is reasonable to suppose that remains
F is the transmitted amplitude, and the tunneling probability is
In the tunneling region ( 0 x a ), the WKB approximation gives
But if the barrier is very high and/or very wide, then the coefficient of the exponentially increasing term (C) must be small, and the wave function looks something like Figure 8.4.
量子力学英文格里菲斯Chapter2PPT课件
14
Once we have found the separable solutions, then, we can immediately construct a much more general solution, of the form
It so happens that every solution to the (time dependent) Schrödinger equation can be written in this form — it is simply a matter of finding the right constants (c1, c2, c3, c4, …）so as to fit the initial conditions for the problem at hand.
4
Now the left side is a function of t alone, and the right side is a function of x alone.
5
The only way this can be possibly be true is if both sides are in fact constant, we shall call the separation constant E. Then
But before we get to that we would like to consider further the question:
7
What’s so great about separable solution ?
可分离的解（即 (x,t)=(x) f(t) ）为何如此重要？
After all, most solutions to the (time-dependent)
Once we have found the separable solutions, then, we can immediately construct a much more general solution, of the form
It so happens that every solution to the (time dependent) Schrödinger equation can be written in this form — it is simply a matter of finding the right constants (c1, c2, c3, c4, …）so as to fit the initial conditions for the problem at hand.
4
Now the left side is a function of t alone, and the right side is a function of x alone.
5
The only way this can be possibly be true is if both sides are in fact constant, we shall call the separation constant E. Then
But before we get to that we would like to consider further the question:
7
What’s so great about separable solution ?
可分离的解（即 (x,t)=(x) f(t) ）为何如此重要？
After all, most solutions to the (time-dependent)
量子力学英文课件格里菲斯Charter9
If we want to allow for transitions between one energy level and another, we must introduce a time-dependent potential (quantum dynamics).
There are precious few exactly solvable problems in quantum dynamics.
where
We’ll assume that Eb > Ea , so 0 0. 0 —— transition frequency
So far, everything is exact: We have made no assumption about the size of the perturbation.
The only difference is that ca and cb of Eq.[9.4] are now functions of t :
Now, the whole problem is to determine ca(t) and cb(t) as functions of time.
dcb/dt, from Eq.[9.8] we have :
and hence
Eqs.[9.10] and [9.11] determine ca(t) and cb(t); taken together, they are completely equivalent to the (time-dependent) Schrodinger equation, for a twolevel system.
However, if the time-dependent portion of the Hamiltonian is small compared to the time independent part. it can be treated as a perturbation.
量子力学英文名词
物理学名词中英文对照
斯特藩-玻耳 Stefan-Boltzmann law 兹曼定律 斯特藩常量 Stefan constant 维恩位移定律 Wien displacement law 瑞利-金斯公式 Rayleigh-Jens formula 普朗克辐射公式 Planck radiation formula 普朗克常量 Planck constant
附 录
5
物理学
第五版
物理学
第五版
物理学名词中英文对照
能带 基态 激发态 弗兰克赫兹实验 德布罗意波 德布罗意波长
energy band ground state excitation state Franck-Hertz experiment De Broglie wave De Broglie wavelength
附
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物理学
第五版
物理学
第五版
物理学名词中英文对照
普丰得系 玻尔量子 化条件 玻尔氢原子 玻尔频率条件 玻尔半径 能级
Pfund series Bohr quantization condition Bohr hydrogen atom Bohr frequency condition Bohr radius energy level
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物理学
第五版
物理学
第五版
物理学名词中英文对照
康普顿效应 康普顿散射 康普顿波长 反冲电子 莱曼系 帕邢系 布拉开系
Compton effect Compton scattering Compton wavelength recoil electron Lyman series Paschen series Brackett series
Chapter 2 The Schrodinger Equation 量子力学英文教案课件
The principle of the superposition state back
（1） The principle of the superposition state （2） The wave function in momentum space
ω( r, t )= {dW(r, t )/ dτ}= C |Ψ (r,t)|2
W(t)=∫V dW =∫Vω( r, t )dτ= C∫V|Ψ (r,t)|2 dτ
University of Electronic Science and Technology of China
2005-3-1
Prof. Zhang Xiaoxia©
back
Chapter 2 The Schrodinger Equation
The Interpretation of the Wave Function The principle of the superposition state Average value of dynamics quantity and Differential Operators Schrodinger Equation Time-independent Schrodinger Equation The Heisenberg Uncertainty Relation
p (r ,t)[2 1]3/2e i[p •r E]t p (r )e iEt
where
1
p(r)[2]3/2
i[p•r]
e
University of Electronic Science and Technology of China
2005-3-1
Prof. Zhang Xiaoxia©
量子力学入门 英语
Einstein
In 1913，Bohr proposed that electrons travel only in certain orbits and that any atom could exist only in a discrete set of stable states，and developed a new theory of the atom. 1913年，波尔提出了电子是按固 定轨道运行和电子只能处于一些 离散的稳定状态的假设。在此基 础上，他推动了新的原子理论的 发展。
1900年，普朗克提出能量的发射和吸 收是按“一份一份”进行的假说 ，这 个假说成功的解释了黑体辐射模型。
Planck
• in 1905 ，Einstein used Planck’s quantum hypothesis realistically to explain the photoelectric effect. • 1905年，爱因斯坦用普朗克 的量子假设成功地解释了光 电效应。
Can a particle escape from the black hole ? It is still a unsolved mystery . 一个粒子能成黑洞中跑出来吗？这至今是个未解之谜。
Round two : About Velocity 第二回合：关于速度 第二回合：关于速度 According to the relativity theory , nothing can travel faster than light velocity . But quantum entanglement shows us that one particle can affect another with no time , no information. 根据相对论，没有什么东西比光速还快。但量子纠缠态 向我们展示，一个粒子能在瞬间影响其它地方的粒子， 并且不需要传递什么作用力。
In 1913，Bohr proposed that electrons travel only in certain orbits and that any atom could exist only in a discrete set of stable states，and developed a new theory of the atom. 1913年，波尔提出了电子是按固 定轨道运行和电子只能处于一些 离散的稳定状态的假设。在此基 础上，他推动了新的原子理论的 发展。
1900年，普朗克提出能量的发射和吸 收是按“一份一份”进行的假说 ，这 个假说成功的解释了黑体辐射模型。
Planck
• in 1905 ，Einstein used Planck’s quantum hypothesis realistically to explain the photoelectric effect. • 1905年，爱因斯坦用普朗克 的量子假设成功地解释了光 电效应。
Can a particle escape from the black hole ? It is still a unsolved mystery . 一个粒子能成黑洞中跑出来吗？这至今是个未解之谜。
Round two : About Velocity 第二回合：关于速度 第二回合：关于速度 According to the relativity theory , nothing can travel faster than light velocity . But quantum entanglement shows us that one particle can affect another with no time , no information. 根据相对论，没有什么东西比光速还快。但量子纠缠态 向我们展示，一个粒子能在瞬间影响其它地方的粒子， 并且不需要传递什么作用力。
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
量子力学英文课件格里菲斯Chapter5
Moreover, if a system starts out in such a state, it will remain in such a state !
The new law (symmetrization requirement) is that:
for identical particles the wave function is not merely allowed, but required to satisfy Eq.[5.14] , with the plus sign for bosons and the minus sign for fermions.
The statistical interpretation carries over in the obvious way:
Hale Waihona Puke is the probability of finding particle 1 in the volume d3r1 and particle 2 in the volume d3r2 . Evidently must be normalized in such a way that
and E is the total energy of the system.
Suppose particle 1 is in the (one-particle) state a(r), and particle 2 is in the state b(r).
In that case, (r1,r2) is a simple product:
Quantum mechanics neatly accommodates the existence of particles that are indistinguishable in principle : We simply construct a wave function that is noncommittal as to which particle is in which state. There are actually two ways to do it:
量子力学学习课件第三章英文版
(1) hermitian? In this case: As is the usual polar coordinate:
On the interval
(2) The eigenvalue equation, The general solution is By using periodic boundary condition
Therefore, the set of all square-integrable functions, on a specified interval,
constitutes a (much smaller) vector space.
Mathematicians call it L2(a,b), while physicists call it Hilbert space.
the addition and the inner product
The inner product of two vectors, which generalizes the dot product in three dimensions, is defined by
2. Linear transformations
In an N-dimensional space, the vector is represented by a N-number of its components, with respect to a specified orthonormal basis:
We can define operations on vectors:
Some important concepts
On state
we measure an observable Q.
On the interval
(2) The eigenvalue equation, The general solution is By using periodic boundary condition
Therefore, the set of all square-integrable functions, on a specified interval,
constitutes a (much smaller) vector space.
Mathematicians call it L2(a,b), while physicists call it Hilbert space.
the addition and the inner product
The inner product of two vectors, which generalizes the dot product in three dimensions, is defined by
2. Linear transformations
In an N-dimensional space, the vector is represented by a N-number of its components, with respect to a specified orthonormal basis:
We can define operations on vectors:
Some important concepts
On state
we measure an observable Q.
量子力学原理_[英文版](P.A.M.Dirac[著])PPT模板
PPT模板](https://img.taocdn.com/s3/m/fe26e49ecf84b9d529ea7a16.png)
§37电子的自 旋
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§38在有心力 场中的运动
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§36角动量的 性质
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§39氢原子的 能级
第6章初等应用
§40选择定则 §41氢原子的塞曼效应
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第7章微扰理论
第7章微扰理 论
§42概述
§47反常塞
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§43微扰引 起的能级 02 变 化
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§7线 性算符
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§9本征值 与本征矢
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§12普遍 的物理解
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第2章动力学变量 与可观察量
§13对易性与相容性
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第3章表象理论
第3章表象理 论
1 §14基矢量
与散射
§62对光子 的应用
§63光子与 原子间的相
互作用能
§59玻色子 系集
§60玻色子 与振子之间
的联系
§61玻色子 的发射与吸
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第10章辐射理论
§65费米子系集
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第11章电子的相对论性理论
第11章电子的相对论性理论
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§66粒子 的相对论
性处理
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§67电子 的波方程
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§68洛伦 兹变换下 的不变性
量子力学原 理:[英文 版 ] ( P. A . M . D i r ac[著])
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第1章叠加原理
第1章叠加 原理
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§35角动量
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§38在有心力 场中的运动
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§36角动量的 性质
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§39氢原子的 能级
第6章初等应用
§40选择定则 §41氢原子的塞曼效应
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第7章微扰理论
第7章微扰理 论
§42概述
§47反常塞
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曼 效 应 06
§43微扰引 起的能级 02 变 化
§46与时
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第2章动力学变量与可观察量
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可 观 察 量
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§7线 性算符
§10可 观察量
§8共 轭关系
§11可观 察量的函
数
§9本征值 与本征矢
量
§12普遍 的物理解
释
第2章动力学变量 与可观察量
§13对易性与相容性
03
第3章表象理论
第3章表象理 论
1 §14基矢量
与散射
§62对光子 的应用
§63光子与 原子间的相
互作用能
§59玻色子 系集
§60玻色子 与振子之间
的联系
§61玻色子 的发射与吸
收
第10章辐射理论
§65费米子系集
11
第11章电子的相对论性理论
第11章电子的相对论性理论
A
§66粒子 的相对论
性处理
B
§67电子 的波方程
C
§68洛伦 兹变换下 的不变性
量子力学原 理:[英文 版 ] ( P. A . M . D i r ac[著])
演讲人 2 0 2 X - 11 - 11
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第1章叠加原理
第1章叠加 原理
量子力学英文课件格里菲斯Chapter3
Technically, a Hilbert space is a complete inner product space, and the collection of square-integrable functions is only one example of a Hilbert space. In quantum mechanics, then,
Outline
In the last two chapters, we have stumbled on a number of interesting properties of simple quantum systems. Some of these are ―accidental‖ features of specific potentials (the even spacing of energy levels for the harmonic oscillator, for example), but others seem to be more general, and it would be nice to prove them once and for all (the uncertainty principle, for instance, and the orthogonality of stationary states).
A set of functions, { fn }, is orthonormal if they are normalized and mutually orthogonal:
Finally, a set of functions is complete if any other function g(x) (in Hilbert space) can be expressed as a linear combination of them:
量子力学英文课件格里菲斯Chapter7
Example 2. Suppose we’re looking for the ground state energy of the delta function potential:
Again, we already know the exact answer (Eq.[2.109]): Eg= m2/2ħ2. (i) As before, we’ll use a gaussian trial wave function with a parameter b (Eq.[7.2]). We’ve already determined the normalization and calculated T; all we need is
Of course, we already know the exact answer, in this case (Eq.[2.49]): Eg = (1/2)ħ; but this makes it a good test of the method. (i) We might pick as our “trial”(尝试) wave function the gaussian,
where A is determined normalization:
On the one hand, according to the theorem:
On the other hand, the Hamiltonian H of the onedimensional infinite square well is
(ii) Evidently
(iii) and we know that this exceeds Eg for all b. Minimizing it,
量子力学英文课件格里菲斯Chapter4
Outside the well the wave function is zero; inside the well the radial equation says
where
Our problem is to solve this equation, subject to the boundary condition : u(a)=0. The case l = 0 is easy:
In other words, exp[im(+2)]=exp[im], or exp(i2m) =1. From this it follows that m must be an integer :
(ii). The equation [4.20]
may not be so familiar. The solution is
批注本地保存成功开通会员云端永久保存去开通
Outline
The generalization to three dimensions is straight forward. Schrödinger’s equation says
where the Hamiltonian operator H is obtained from the classical energy
contains an extra piece, centrifugal term, (ħ2/2m)[l(l+1)/r2].
It tends to throw the particle outward (away from the origin), just like the centrifugal (pseudo-) force in classical mechanics.
高二物理竞赛课件：量子力学(共14张PPT)
“鬼魅”的量子纠缠（Spooky entanglement）
LAOCOON 2
量子纠缠
➢ 量子纠缠是粒子在由两个或两个以上粒子组成系统中相互影响的现 象，虽然粒子在空间上可能分开；
➢ 纠缠是关于量子力学理论最著名的预测，它描述了两个粒子互相纠 缠，即使相距遥远距离，一个粒子的行为将会影响另一个的状态；
7
量子纠缠态
8
量子远程传态-----“瞬间转移”
量子纠缠通信 Einstein-Podolsky-Rosen (EPR) 对
➢ 采用双光子分发，通信距离增加一倍
Alice
随机地选择 两组解码基
0H
1 V
Bob
1L
0R
10
量子纠缠通信
自由空间的量子纠缠分发通信（青海湖）
量子纠缠通信
自由空间的量子纠缠分发通信（地中海）
➢ 当其中一颗被操作（例如量子测量）而状态发生变化，另一颗也会 即刻发生相应的状态变化。
量子纠缠
非 纠 缠
纠 缠
量子纠缠态
-
随着科学与技术的发展，这个理想实验被证实
5
自然界中的量子纠缠
微观不确定性--->宏观不确定性 “薛定谔的猫”
实验装置
150mW diode 70000 detected coincide
LAOCOON 2
量子纠缠
➢ 量子纠缠是粒子在由两个或两个以上粒子组成系统中相互影响的现 象，虽然粒子在空间上可能分开；
➢ 纠缠是关于量子力学理论最著名的预测，它描述了两个粒子互相纠 缠，即使相距遥远距离，一个粒子的行为将会影响另一个的状态；
7
量子纠缠态
8
量子远程传态-----“瞬间转移”
量子纠缠通信 Einstein-Podolsky-Rosen (EPR) 对
➢ 采用双光子分发，通信距离增加一倍
Alice
随机地选择 两组解码基
0H
1 V
Bob
1L
0R
10
量子纠缠通信
自由空间的量子纠缠分发通信（青海湖）
量子纠缠通信
自由空间的量子纠缠分发通信（地中海）
➢ 当其中一颗被操作（例如量子测量）而状态发生变化，另一颗也会 即刻发生相应的状态变化。
量子纠缠
非 纠 缠
纠 缠
量子纠缠态
-
随着科学与技术的发展，这个理想实验被证实
5
自然界中的量子纠缠
微观不确定性--->宏观不确定性 “薛定谔的猫”
实验装置
150mW diode 70000 detected coincide
复旦量子力学讲义qmapter-PPT精品
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§3.2 Dirac equation
➢4 anti-commute matrices α and β 4×4 matrices
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§3.2 Dirac equation
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§3.2 Dirac equation
➢Conservation law of the probability flux
† , jkc†k
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§3.3 solutions of the free particle
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§3.3 solutions of the free particle
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§3.3 solutions of the free particle
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§3.2 Dirac equation
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§3.2 Dirac equation
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§3.2 Dirac equation
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§3.2 Dirac equation
➢The condition for α and β
1) They must follow the relation
equation
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§3.1 Klein – Gordon equation
➢Lorentz transormation time, space are of the same weight
➢K – G equation
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§3.1 Klein – Gordon equation
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§3.2 Dirac equation
➢4 anti-commute matrices α and β 4×4 matrices
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§3.2 Dirac equation
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§3.2 Dirac equation
➢Conservation law of the probability flux
† , jkc†k
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§3.3 solutions of the free particle
2020/5/29
§3.3 solutions of the free particle
2020/5/29
§3.3 solutions of the free particle
2020/5/29
2020/5/29
§3.2 Dirac equation
2020/5/29
§3.2 Dirac equation
2020/5/29
§3.2 Dirac equation
2020/5/29
§3.2 Dirac equation
➢The condition for α and β
1) They must follow the relation
equation
2020/5/29
§3.1 Klein – Gordon equation
➢Lorentz transormation time, space are of the same weight
➢K – G equation
2020/5/29
§3.1 Klein – Gordon equation
2020/5/29
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