1.225 U k 2d sin
U1 2
The electrons are waves！
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Chapter 22 Introduce of Quantum Mechanics
汤姆逊实验G.P. Thomson Experiment (1928)
Electron gun
Electron beam
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Chapter 22 Introduce of Quantum Mechanics
§22.1.2 物质波的实验验证——电子的衍射
Filament to emits electrons
Electron Diffra and Germer’s Experiment(1927)
The electrons are waves！
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Chapter 22 Introduce of Quantum Mechanics
•Experiment results II
1.225 nm U
3.061
2
3
4
5
6
7
8
9
代入
2d sin k
Diffraction pattern from Nickel crystal surface at the same and different U
Example 2：What is the de Broglie wavelength of electrons (mass m= 9.110-31kg) with potential U? 1. 非相对论情形In the case of non-relativity v<<c
1 mv 2 eU 2
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Chapter 22 Introduce of Quantum Mechanics
Louis de Broglie
The Nobel Prize in Physics 1929
Biography (1892-1987)
Prince Louis-Victor de Broglie of the French Academy, Permanent Secretary of the Academy of Sciences, and Professor at the Faculty of Sciences at Paris University, was born at Dieppe (Seine Inférieure) on 15th August, 1892, the son of Victor, Duc de Broglie and Pauline d'Armaillé. After studying at the Lycée Janson of Sailly, he passed his school-leaving certificate in 1909. He applied himself first to literary studies and took his degree in history in 1910. Then, as his liking for science prevailed, he studied for a science degree, which he gained in 1913. He was then conscripted for military service and posted to the wireless section of the army, where he remained for the whole of the war of 1914-1918. During this period he was stationed at the Eiffel Tower, where he devoted his spare time to the study of technical problems. At the end of the war Louis de Broglie resumed his studies of general physics. While taking an interest in the experimental work carried out by his elder brother, Maurice, and co-workers, he specialized in theoretical physics and, in particular, in the study of problems involving quanta. Louis de Broglie died on March 19, 1987.
2 r n
h/mv
mvr n
——Bohr’s result
We find
德布罗意用物质波的概念成功地解 释了玻尔提出的 轨道量子化条件 。
n=3
n=4
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Chapter 22 Introduce of Quantum Mechanics
是粒子还是波？ Example：What is the de Broglie wavelength of a bullet (mass m=0.01kg) with a speed v=300m/s? h h 6.63 10 34 2.21 10 34 m 0.01 300 p m
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Chapter 22 Introduce of Quantum Mechanics
The Nobel Prize in Physics 1937
C.J. Davisson
G.P. Thomson
13
通过实验发现受电子照射的晶体中的衍射现象
Chapter 22 Introduce of Quantum Mechanics
Chapter 22 Introduce of Quantum Mechanics
Chapter 22 量子力学基本原理Introduce of Quantum Mechanics
扫描电子显微镜工作原理？
A scanning eletron micrograph reveals bacteria magnified 2,000 times.
Too small to measure
If m=1g，v=1cm/s, the particle wavelength is
h 6.62 1034 29 3 6.62 10 m 2 mv 10 10
Too small to measure either!!
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Chapter 22 Introduce of Quantum Mechanics
The wave nature of particles?
Seen under an electron microscope are Staphylococcus aureus bacteria from a group that is resistant to antibiotics
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Chapter 22 Introduce of Quantum Mechanics
2. 相对论情形In the case of relativity v~c
2 4 E 2 p 2 c 2 m0 c
2 2 4 E m 2 0c p 2 c
E Ek m0c 2
h p
Ek eU
hc Ek2 2 Ek m0 c 2
v c
h 2m0 eU

E hf
•自由粒子以单色平面波传播
( x, t ) 0 e
i (t kx )
0e
i ( px Et )
Caution: The relationship E=hf must be carefully applied to nonzero-rest-mass particles. Unlike a photon, they do 4 not travel at speed c.
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Chapter 22 Introduce of Quantum Mechanics
22.1.1 德布罗意假设De Broglie Waves De Broglie Hypothesis
实物粒子具有波动性
momentum p=mv in exactly the same way as for a photon.
Gold foil
screen
The upper diffraction pattern was made by a beam of x-ray passing through thin aluminum foil. The lower diffraction was made by a beam of electrons passing through the same foil
约恩逊实验C. Jönsson Experiment
1961年C. Jö nsson运用铜箔中形成的2-5条细缝 得到了电子的多缝干涉图样。
a

Slit
Other Experiments
1930 年 艾 斯 特 曼 (Estermann) 、 斯 特 恩 (Stern)、和他们的同事们证实了普通原子 具有波动性。后来实验又验证了质子、中 子等实物粒子都具有波动性。
Chapter 22 量子力学的基本原理
§22.1 波函数的统计解释Wave Function and Its Interpretation §22.2 不确定度关系Uncertainty Relations §22.3 态叠加原理 §22.4 薛定谔方程The SchrÖdinger Equation §22.5 力学的算符表示
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Chapter 22 Introduce of Quantum Mechanics