1. 20 世纪初物理 天空上有几朵乌云 第八讲 量子力学绪论 量子力学的诞生过程 “ 概率幅 ” 的引入

2. 量子力学的诞生过程 It was beginning from the issue about light ……  Newton theory: Light is made up of tiny balls.  Maxwell theory: Light is a kind of wave.  But there were some problems that can not be explained by both of theories above. Blackbody Radiation Photoelectric Effect Compton scattering Spectrum of Hydrogen atom

3. Planck’s explanation of the blackbody radiation In 1900, Planck explained the blackbody radiation by supposing that light is made up of many photons.

4. 量子力学的诞生过程 In 1905 Einstein’s Explanation of Photoelectric Effect -V stop = Constant

5. Classically If you double light intensity you would expect -2.0 VV I eV stop = Ke

6. Einstein’s Explanation of Photoelectric Effect

7. In 1923 Compton scattering X-ray source Target Crystal (selects wavelength) Collimator (selects angle) θ A.H. Compton, Phys. Rev. 22 409 (1923) Result: peak in scattered radiation shifts to longer wavelength than source. Amount depends on θ (but not on the target material).

8. COMPTON SCATTERING (cont) Compton’s explanation: “billiard ball” collisions between particles of light (X-ray photons) and electrons in the material Classical picture: oscillating electromagnetic field causes oscillations in positions of charged particles, which re-radiate in all directions at same frequency and wavelength as incident radiation. Change in wavelength of scattered light is completely unexpected classically θ BeforeAfter Electron Incoming photon scattered photon scattered electron Oscillating electron Incident light wave Emitted light wave

9. Conservation of energyConservation of momentum From this Compton derived the change in wavelength θ BeforeAfter Electron Incoming photon scattered photon scattered electron COMPTON SCATTERING (cont)

10. 人们终于承认光还有 “ 粒子性 ” ，当然早 就承认光也有 “ 波性 ” How about electrons--the tiny particles of matter ?  Newton theory thought it should be a particle.  But there were also a few problems that can not be explained by classical physics…… Spectrum of Hydrogen atom The scattering of electrons on a surface of crystal

11. DavissonG.P. Thomson Davisson, C. J., "Are Electrons Waves?," Franklin Institute Journal 205, 597 (1928) The Davisson-Germer experiment: scattering a beam of electrons from a Ni crystal. Davisson got the 1937 Nobel prize. At fixed accelerating voltage (fixed electron energy) find a pattern of sharp reflected beams from the crystal At fixed angle, find sharp peaks in intensity as a function of electron energy G.P. Thomson performed similar interference experiments with thin-film samples θiθi θiθi ELECTRON DIFFRACTION The Davisson-Germer experiment (1927)

12. 1924 年 de Broglie 战战兢兢提出一个 大胆的假设：电子也有 “ 波性 ” 对应光波的粒子性大胆的假设：光波也 有 “ 粒子性 ”—— 光子

13. The strange (and beautiful) world of Quantum Mechanics Very frightening Just beautiful!

14. Duality Whom do you see in this picture? A young girl? Old woman?

15. De Broglie - Heisenberg de Broglie Heisenberg

16. From work of Eigler (IBM)

17. With particles (bullets) Behavior of bullets is easy to understand - LUMPINESS! Two Slit experiments I1I1 I2I2 I 12

18. With waves (water waves) I1I1 I2I2 I 12

19. Waves interfere! NO LUMPINESS!  1 +  2   12

20. LUMPINESS! INTERFERENCE! With electrons Electrons are like bullets - lumps I1I1 I2I2 I 12

21. 概率幅 —— 电子双缝干涉实验 预备知识 不干涉的宏观粒子 干涉的光波 不干涉的光波 电子的双缝实验证明电子具有 “ 波 ” 的干涉性 对电子 “ 波 ” 的干涉现象的描述 寻找解释电子 “ 波 ” 的干涉现象的方法 引入新概念 — 概率幅 probability amplitude

22. Double-Slit Experiment with a machine gun! 不干涉的宏观粒子

23. Double-Slit Experiment to illustrate wave nature of light 干涉的光波

24. Double-Slit Experiment to illustrate wave nature of light 干涉的光波

25. Double-Slit Experiment with non-interference light sources 不干涉的光波

26. Double-Slit Experiment with electronics Electrons behave like waves! The interference pattern is the distribution of the probability of position at which electrons arrive.

27. Double-Slit Experiment with electronics

28. Bologna 1974 Hitachi 1989 1961, Jönsson, Zeitschrift für Physik 161 454 1974, P. Merli, G. Missiroli and G. Pozzi in Bologna in 1974 1989,Hitachi (A Tonomura et al). Demonstration of single-electron buildup of an interference pattern Am. J. Phys. 57

29. Neutrons: A Zeilinger et al. 1988 Reviews of Modern Physics 60 1067-1073 He atoms: O Carnal and J Mlynek 1991 Physical Review Letters 66 2689-2692 C 60 molecules: M Arndt et al. 1999 Nature 401 680- 682 With multiple-slit grating Without grating EXPERIMENTAL RESULTS Interference patterns can not be explained classically - clear demonstration of matter waves Fringe visibility decreases as molecules are heated. L. Hackermüller et al. 2004 Nature 427 711-714

30. Double-Slit Experiment with electronics Electron interference pattern after (a)8 electrons (b)270 electrons, (c) 2000 electrons, (d) 6000 electrons Hitachi 1989, Demonstration of single-electron buildup of an interference pattern

31. Double-slit experiment succeeds in a single hydrogen molecule Lawrence Berkeley National Laboratory (LBNL; Berkeley, CA) D Akoury, K Kreidi, T Jahnke, et al., Science 318, 949 (Nov. 9, 2007).

32. How to explain it ? ! In this sense, Electrons behave like waves! The probability of arrival of these electrons is distributed like the distribution of intensity of a wave.

33. How to explain it ? ! It does work !!! Proposition A: Each electron either goes through hole 1 or it goes through hole 2. Then it should be Let’s do some mathematics! Let Where the complex function Ψ 1 is related to the effect with only hole 1 open, the complex function Ψ 2 is related to the effect with only hole 2 open. How about this one? Let Anyway, Proposition A is false. It is not true that the electrons go through hole 1 or hole 2.

34. Watching the electrons! Here is what we see: every time that we hear a “click” from our electron detector, we also see a flash of light either near hole 1 or near hole 2, but never both at once! Experimentally, proposition A is necessarily true!!!

35. Continue to watch the electrons! Don’t use such bright light source!  If the electrons are not seen, we have interference! If we use “gentler” light perhaps we can avoid disturbing the electrons so much.  We begin to get some interference effect when we make the wavelength longer than the distance between our holes. It is impossible to arrange a light in such a way that one can tell which hole the electron went through, and at the same time not disturb the interference patter.

36. That ‘s it ! You have to take it! It is impossible to design an apparatus to determine which hole the electron passes through, that will not at the same time disturb the electrons enough to destroy the interference patter. We must assume that it describes a basic characteristic of nature

37. SUMMARY The probability of an event in an ideal experiment is given by the square of the absolute value of a complex number Ψwhich is called the probability amplitude. When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately. If an experiment is performed which is capable of determining whether one or another alternative is actually taken, the probability of the event is the sum of probabilities for each alternative. The interference is lost. P= probability Ψ=probability amplitude