Louis de Broglie

1. Louis de Broglie If light, which we thought of as a wave, behaves as a particle, then maybe things we think of as particles behave as waves… photo from http://www.aip.org/history/heisenberg/p08.htm

2. Energy/Frequency and Momentum/Wavelength Relations for a Photon Energy/Frequency and Momentum/Wavelength Relations for an Electron/Proton/Apple Pie/Ford Taurus

3. What Exactly is Waving? • For a photon... • electric and magnetic fields • You can measure them if fis small enough. • For visible light, you can see that it is a wave indirectly. • For a massive particle • You can’t measure them --- even in theory! • They are complex! • How do we know that there’s really a wave?

4. How might I verify that my Ford is a wave? Interference Diffraction

5. Thought Question Which of the following would be the easiest particle to use if I wanted to see a matter-wave diffraction pattern? • A car moving at 100 mph • A car moving at 1 mph • A 1 MeV electron • A 10 eV electron • What was the question?

6. Wavelength of a Ford So, why didn't we notice the wave nature of matter before?

7. Wavelength of a 10 eV Electron This is still tiny! Where have we come across something this small before?

8. Davisson and Germer photo from http://faculty.rmwc.edu/tmichalik/davisson.htm

9. Cesium Interferometer

10. Interference of BEC

11. C60 Interference Recent results from Vienna group of Anton Zielinger: The interfering particle: Buckyballs Apparatus Not only more mass, but more degrees of freedom too! Interference fringes! http://www.quantum.univie.ac.at/

12. Pure Sine Wave y=sin(5 x) Power Spectrum

13. “Shuttered” Sine Wave y=sin(5 x)*shutter(x) Power Spectrum

14. “Thin” Gaussian y=exp(-(x/0.2)^2) Power Spectrum

15. “Fat” Gaussian y=exp(-(x/2)^2) Power Spectrum

16. Femtosecond Laser Pulse Et=0=sin(10 x)*exp(-x^2) Power Spectrum

17. Uncertainty in a Classical Wave

18. Uncertainty Relations Classical Wave Position – Momentum Energy – Time

19. Wave-Particle Duality • Things act as wave when propagating • or, in other words, we use waves to make predictions as to what we will find when we make our measurement. • Things act as waves when we measure wave-like properties. • Things act as particles when we measure particle-like properties • Example: BEC interference --- theorists confused about “undefined phase”

20. WHERE CAN YOU FIND TRUTH? • A ride with a tow truck driver • An article on idiots filled with . . . the word • Peer reviewers trying to sound smart • A Buddhist Sunday school teacher

21. WHERE CAN YOU FIND TRUTH? "We believe in all truth, no matter to what subject it may refer. No sect or religious denomination [or, I may say, no searcher of truth] in the world possesses a single principle of truth that we do not accept or that we will reject. We are willing to receive all truth, from whatever source it may come; for truth will stand, truth will endure." -- Joseph F. Smith

22. What is stuff made of?

23. Rutherford’s Experiment Shooting bullets at jello . . .

24. Radiating Atoms

25. Bohr’s Theory • He did not think in terms of waves • He simply postulated that • There are orbits in which the electron doesn’t radiate. • The light released when an electron changes orbits is a photon with an energy equal to the difference in energy of the two orbits • He further postulated that the orbits were circularwith quantized angular momentum of

26. Hydrogen

27. Balmer series—An electron falls to the n=2 energy state and a photon is emitted. n=6 to n=2 410 nm Violetn=5 to n=2 434 nm Violetn=4 to n=2 486 nm Bluegreenn=3 to n=2 656 nm Red

28. An electron absorbs a photon and jumps to a higher energy level.

29. The green emission line in hydrogen is a transition from an excited state n=4 to n=2. The red line must be a transition from ______ to n=2. • n=1 • n=2 • n=3 • n=4 • n=5

30. Which transition in hydrogen gives off the shortest wavelength (highest energy) of radiation. • n=2 to n=1 • n=3 to n=2 • n=6 to n=3 • n=8 to n=4 • n=100 to n=5

31. Bohr Theory Successes/Failures • Predicts emission and absorption lines of hydrogen and hydrogen-like ions • Predicts x-ray emissions (Moseley’s law) • Gives an intuitive picture of what goes on in an atom • The correspondence principle is obeyed... sort of • It can’t easily be extended to more complicated atoms • No prediction of rates, linewidths, or line strengths • Fine structure (and hyperfine structure) not accounted for • How do atoms form molecules/solids? • Where did it come from? There must be a more general underlying theory! • It gave hints of a new, underlying theory

32. Schorodinger’s Idea • Probability waves • Tells the probability of finding a particle at some particular place at a particular time. • The electron is more likely to be where the amplitude of the wave is high.

33. =i

36. Match the spectrum to the one you see. H He O Ne http://astro.u-strasbg.fr/~koppen/discharge/ http://www.colorado.edu/physics/2000/quantumzone/index.html http://jersey.uoregon.edu/vlab/elements/Elements.html

37. Tunneling

38. Cross-section of a MOSFET transistor gate consisting of a 2 nm thick amorphous silicon oxide layer between crystalline silicon (top) and polycrystalline silicon (bottom). Individual atomic columns and dumbbells are clearly visible. The image provides data on the precise location and roughness of the gate oxide interface, while revealing how the silicon crystal structure is locally affected near the interface. (Source: FEI Co.)

39. STM image http://www.almaden.ibm.com/vis/stm/gallery.html

40. STM image http://www.almaden.ibm.com/vis/stm/gallery.html

41. STM image http://www.almaden.ibm.com/vis/stm/gallery.html

42. Postulates of Quantum Mechanics • Every physically-realizable system is described by a state function ψ that contains all accessible physical information about the system in that state • The probability of finding a system within the volume dv at time t is equal to |ψ|2dv • Every observable is represented by an operator which is used to obtain information about the observable from the state function • The time evolution of a state function is determined by Schrödinger’s Equation