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,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 RadiationPhotoelectric
2、 EffectCompton scatteringSpectrum of Hydrogen atom,Plancks explanation of the blackbody radiation,In 1900, Planck explained the blackbody radiation by supposing that light is made up of many photons.,量子力学的诞生过程,In 1905 Einsteins Explanation of Photoelectric Effect,-Vstop= Constant,Classically,If you
3、double light intensity you would expect,-1.0,-2.0,DV,I,eVstop = Ke,Einsteins Explanation of Photoelectric Effect,In 1923 Compton scattering,A.H. Compton, Phys. Rev. 22 409 (1923),Result: peak in scattered radiation shifts to longer wavelength than source. Amount depends on (but not on the target mat
4、erial).,COMPTON SCATTERING (cont),Comptons 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 a
5、t same frequency and wavelength as incident radiation.Change in wavelength of scattered light is completely unexpected classically,Conservation of energy,Conservation of momentum,From this Compton derived the change in wavelength,COMPTON SCATTERING (cont),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 elect
6、rons-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 physicsSpectrum of Hydrogen atomThe scattering of electrons on a surface of crystal,Davisson,G.P. Thomson,Davisson, C. J., Are Electrons Waves?,
7、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 pe
8、aks in intensity as a function of electron energy,G.P. Thomson performed similar interference experiments with thin-film samples,i,i,ELECTRON DIFFRACTIONThe Davisson-Germer experiment (1927),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,The strange (and beautiful) world of Quantu
9、m Mechanics,Duality,A young girl?Old woman?,De Broglie - Heisenberg,From work of Eigler (IBM),With particles (bullets),Two Slit experiments,With waves (water waves),1 + 2 12,With electrons,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 ampl
10、itude,Double-Slit Experiment with a machine gun!,不干涉的宏观粒子,Double-Slit Experimentto illustrate wave nature of light,干涉的光波,Double-Slit Experiment to illustrate wave nature of light,干涉的光波,Double-Slit Experimentwith non-interference light sources,不干涉的光波,Double-Slit Experimentwith electronics,Electrons b
11、ehave like waves!,The interference pattern is the distribution of the probability of position at which electrons arrive.,Double-Slit Experimentwith electronics,Bologna 1974,Hitachi 1989,1961, Jnsson, Zeitschrift fr Physik 161 4541974, P. Merli, G. Missiroli and G. Pozzi in Bologna in 1974 1989 ,Hita
12、chi (A Tonomura et al). Demonstration of single-electron buildup of an interference pattern Am. J. Phys. 57,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,EXPERIMENTAL RESULTS,Interference patterns ca
13、n not be explained classically - clear demonstration of matter waves,Fringe visibility decreases as molecules are heated. L. Hackermller et al. 2004 Nature 427 711-714,Double-Slit Experiment with electronics,Electron interference pattern after 8 electrons270 electrons, (c) 2000 electrons,(d) 6000 el
14、ectrons,Hitachi 1989, Demonstration of single-electron buildup of an interference pattern,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).,How to explain it ?
15、 !,In this sense, Electrons behave like waves!,The probability of arrival of these electrons is distributed like the distribution of intensity of a wave.,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,Lets do s
16、ome mathematics!Let Where the complex function 1 is related to the effect with only hole 1 open, the complex function 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.,Watching the
17、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!,Continue to watch the electrons!,Dont use such bright light source!
18、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 o
19、ne can tell which hole the electron went through, and at the same time not disturb the interference patter.,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 des
20、troy the interference patter.,We must assume that it describes a basic characteristic of nature,SUMMARY,The probability of an event in an ideal experiment is given by the square of the absolute value of a complex number which is called the probability amplitude.When an event can occur in several alt
21、ernative 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=probability amplitude,
