材料物理课件 (2)原子的波动理论

1) statistical hypothesis ∶
dw | |2 dV dV
dw dV Where | ψ | 2 is equal to the chance of finding the subject at a certain time and position.
Based the duality of light ， in 1926, Erwin Schrodinger(薛定谔)from Austria，Werner Karl Heisenberg(海森 伯)and Max Born(马克斯〃玻恩) from German built the quantum mechanics that is theory to help peoples understand the atom s34 x 1.321032 m mV 0.01 500 0.0001
IV、Wave function (波函数)
A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe the momentary states of subatomic particles.
[Example 3] A ball with mass of0.01kg moves at
the velocity about 500m/s 。 If the deviation of the velocity is 0.01% ， what is the deviation of the ball’s position:
A
C

xp x pa sin
h
a Because ：sin , p
,
xp x h
Because the
px
in sub diffraction is bigger :
Uncertainty relation expression
xp h
The uncetainty relation expression, therefore says nothing about the simultaneous measurement of position and momentum.

V
| | 2 dV 1
3)
概率波( 物质波 ) 与 经典波的区别：
0 h 6.63 10 34 34 24 1 10 m 1 10 A mV 1 6.63
∵The wavelength of a particle is too small to be seen by unaided eyes.
h 6.63 10 34 0.8671 1010 m m0V 9.1 10 31 8.4 106
The wavelength of electrons is small so that it can be , so the Electrons can replace the photons used in the microscopes which Have ultra high amplification factors.
1.Wavefunction of particle in free movement
(r , t ) 0e
i ( Et Pr )
2、Statistical explanation of wavefunction
The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states. It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and
III、Uncertainty principle(测不准原理，不确定[度]关系） 1、what is the uncertainty principle
In 1927, the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the D other can be known.
then what is the velocity in atoms. deviation of the electrons’
According the expression
xp h
h 6.63 10 34 v 7.3 106 ( m / s ) mx 9.1 10 31 1010
轨道的概念对微观粒子已失去意义，经典力学的规律 也不再适用。 3、Uncertainty relation expression in common
h 令 2
x p
h 4
xp 2
[Example 2] The magnitude of atoms’ extension 1A，
Louis de Broglie presented his thesis concerning the wave-particle, proposing the idea that all matter displayed the wave-particle duality of photons
II、 Victorde
Broglie hypothesis
1 、 If a particle has the mass of m and moves with the velocity of v ，the particle has the
energy
E h
and Momentum
P
h

Here , ν is the frequency, λ is the wavelength. So a particle with mass of m and velocity of v has the Broglie Wave
Then the atoms ,molecular and neutron were one after the other proved to have the wave property, and the Louis Victorde Broglie’s hypothesis was demonstrated .
2. The wave-particle duality of matter
Peoples originally thought that there were two types in natural matter: matters and fields. All kinds of matters are composed of particles such as atoms and electrons and the light is one of the fields. In 1923，Victorde Broglie (德布罗意) present the hypothesis that the particles in objects has the undulatory property. To prove it, in 1923 he considered the experiment of the electron diffraction and in 1924 he gave the consideration of the electron diffraction experiment in crystal. In 1927， Davisson (戴维孙) –germer(革末) - experiment proved that electrons has the undulatory property ,later， George Paget Thomson (G.P.汤姆孙) and Davisson accomplished the electron diffraction experiment in crystal.
Quantum Mechanics
I、The wave-particle duality theory of light
1. The wave-particle duality of light
微粒说(corpuscular theory of light):In 1672 , Newton 波动说(undulatory theory of light):哥里马第(Grimadi) in Italy is the first man who supported the undulatory theory ;In 1687, 惠更斯(Huygens) further developed the theory In 1905, A.Einstein presented the theory of photons, which shows that the light has both the undulatory property and the corpuscular property. That is the wave-particle duality of light. Mass–energy equivalence ( In Relativity )
h h P mv
德布罗意公式
这种波叫德布罗意波，或称为物质波。
[Example 1] (1) If a particle with the mass of 1kg moves with the velocity of 6.63m/s, how long is its wavelength?(2) How long is the wavelength of the electron with kinetic energy of 200eV。
X
2、For an example（ Electrons' Diffraction ）
the standard deviation of the X-distribution：
B
a
px
p
x a
the standard deviation of P：
O

p
y
px p sin （first diffraction picture）
2
2) This leads to thenormalization condition:
since the probability of a measurement of the particle's position yielding a value in the all position in the space range is unity(probability is 100% in all position).