Wavelike Properties of Matter in Physics

1. Physics 222 David D. Allred

2. Adapted fromAdapted from

3. Wavelike properties of matter Class 8-1-4: (ThT Q)

4. Did you complete at least 70% of Chapter 3: 1-3? • Yes B. No Review Adapted fromAdapted from

5. In our reference frame the beam droops • It happens near stars, too • http://www.theory.caltech.edu/people/patricia/lclens.html • And helps show dark matter. http://apod.nasa.gov/apod/ap080917.html Adapted fromAdapted from

6. Gravitational lensing http://www.nature.com/nature/journal/v417/n6892/fig_tab/417905a_F1.html Adapted fromAdapted from

7. http://www.utahskies.org/HST/Archives/misc.html The Gravitational Lens G2237 + 0305The European Space Agency's Faint Object Camera on board NASA's Hubble Space Telescope has provided astronomers with the most detailed image ever taken of the gravitational lens G2237 + 0305—sometimes referred to as the "Einstein Cross". The photograph shows four images of a very distant quasar which has been multiple-imaged by a relatively nearby galaxy acting as a gravitational lens. The angular separation between the upper and lower images is 1.6 arc seconds.The quasar seen here is at a distance of approximately 8 billion light years, whereas the galaxy at a distance of 400 million light years is 20 times closer. The light from the quasar is bent in its path by the gravitational field of the galaxy. This bending has produced the four bright outer images seen in the photograph. The bright central region of the galaxy is seen as the diffuse central object. Adapted fromAdapted from

8. Gravitational lensinghttp://www.astronomy.org.nz/aas/MonthlyMeetings/MeetingOct2002.asp http://www.physics.brown.edu/physics/demopages/Demo/astro/demo/grvlns8.jpg Adapted fromAdapted from

9. de Broglie Photons: p=h/λ Particle: λ=h/p Hint: If the particle is going slow (K=½p2/m) Adapted fromAdapted from

10. Quick Writing Assignment • In one minute, write a short, clear, and concise paragraph which explains why the Compton effect suggests that light is quantized. Adapted fromAdapted from

11. Puzzles at the Beginning of the Twentieth Century • Null result of the Michelson-Morley Experiment • Ultraviolet Catastrophe • Photoelectric Effect • Maxwell’s Equations Spell the Demise of Atoms! • Discrete atomic emission lines Adapted fromAdapted from

12. Radiating Atoms Adapted fromAdapted from

13. Puzzles at the Beginning of the Twentieth Century • Null result of the Michelson-Morley Experiment • Ultraviolet Catastrophe • Photoelectric Effect • Maxwell’s Equations Spell the Demise of Atoms! • Discrete atomic emission lines Adapted fromAdapted from

14. The Hydrogen Spectrum The Balmer Series Adapted fromAdapted from

15. Quiz Question Where did de Broglie get his equation for the wavelength of a massive particle? A – From special relativity B – It is the same equation used for light. C – It is the same equation used for sound waves traveling through a medium with mass. D – From the principle of least action E – He found it on the internet. Adapted fromAdapted from

16. 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 Adapted fromAdapted from

17. Energy/Frequency and Momentum/Wavelength Relations for a Photon Remember from 220 ... or or Adapted fromAdapted from

18. Energy/Frequency and Momentum/Wavelength Relations for an Electron/Proton/Apple Pie/Ford Taurus or or Adapted fromAdapted from

19. Day 9: Vernal equinox 09-22-2008 @9:39 MDT 3.4 Phase and Group Velocities p 99 A group of waves need not have the same velocity as the waves themselves 3.5 Particle Diffraction p 104 An experiment that confirms the existence of de Broglie waves 3.6 Particle in a Box p 106 Why the energy of a trapped particle is quantized (3.2 Waves of What? Waves of probability)

20. Public Star Party and Opening Social • Get to know the night sky • Look through BIG telescopes • View spiral structure in galaxies! • See nebulas of all types • Watch the moons of Jupiter move • And a whole lot more (no, really, we’re not just saying this - there really is a whole lot more!) When: Friday, Sept. 26 8 - 11pm Where: Big Springs Park What: Telescopes, dark sky, food Directions to Big Springs Park: Head up Provo Canyon. Take a right at Vivian Park. Go through Vivian Park and up the canyon a little over 3 miles. Look for a sign for the star party. Dress warm! Bring your friends. Adapted fromAdapted from

21. Did you complete at least 50% of Chapter 3: 4-6? • Yes B. No Review Adapted fromAdapted from

22. Draw light cone • For electron accelerated to 511 keV in 20 cm Adapted fromAdapted from

23. The Wave Equation: Which satisfy the Wave equation? pp • y = y0sin(kx- ωt) • y = y0e-a(x- vt)²; (Gaussian) • Any f(kx- ωt) • All three • Only A and B Adapted fromAdapted from Adapted fromAdapted from

24. 3.4 Phase and Group Velocities A group of waves need not have the same velocity as the waves themselves

25. Adapted fromAdapted from

26. Consider this experiment: • Throwing a pebble in a still pool. • http://en.wikipedia.org/wiki/Group_velocity • Note green dots mark the beginning and ends of the group of waves but the red dots mark the top of a given wave • If you only had one group of waves, what would it be like? • Why does this work this way? Adapted fromAdapted from

27. Dispersion • Prism: breaks up white light. How? • Refractive index n and velocity of light? • n= c/v • v(λ) = c/n(λ) • v(k) = c/n(k) Adapted fromAdapted from

28. What does dispersion have to do with Matter-waves? • Dispersion means that the velocity depends on the wavelength, or k or frequency. • Look at space-time diagrams. (On blackboard) • Definition of phase and group velocities. • Problem 6-1 (draw the dispersion relationship) Adapted fromAdapted from

29. (draw the dispersion relationship) • Which one? Adapted fromAdapted from

30. Just a note... For a photon But... Adapted fromAdapted from

31. What Exactly is Waving? • For a photon... • electric and magnetic fields • You can measure them if º is 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? Adapted fromAdapted from

32. How might I verify that my Ford is a wave? Interference Diffraction Adapted fromAdapted from

33. Thought Question • Which of the following would be the easiest particle to use if I wanted to see a matter-wave diffraction pattern? 1: A car moving at 100 mph 2: A car moving at 1 mph 3: A 1 MeV electron 4: A 1 keV electron 5: What was the question? Adapted fromAdapted from

34. Wavelength of a Ford So, why didn't we notice the wave nature of matter before? Adapted fromAdapted from

35. Wavelength of a 10 eV Electron This is still tiny! Where have we seen wavelengths this small before? Adapted fromAdapted from

36. 3.5 Particle Diffraction An experiment that confirms the existence of de Broglie waves Adapted fromAdapted from

37. Adapted fromAdapted from

38. Davisson and Germer Adapted fromAdapted from photo from http://faculty.rmwc.edu/tmichalik/davisson.htm

39. Quiz Question Why did Davison and Germer heat their nickel target? A – To induce thermal emission of electrons B – To remove oxide contamination C – To study the thermal expansion coefficient of pure nickel D – To produce blackbody radiation E – To keep their graduate students from sitting on it (ouch, that’s hot!) Adapted fromAdapted from

40. Bragg Diffraction Adapted fromAdapted from

41. Bragg Diffraction Why so many peaks? Adapted fromAdapted from

42. 1. Many orders (n=1,2,3,4,...) 2. Many Bragg planes Adapted fromAdapted from

43. Bragg Diffraction Why circles instead of spots? Adapted fromAdapted from

44. Adapted fromAdapted from

45. Scanning the Energy of the Electrons Adapted fromAdapted from

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47. de Broglie Photons: p=h/λ Particle: λ=h/p Hint: If the particle is going slow (K=½p2/m) Adapted fromAdapted from

48. Quick Writing Assignment • In one minute, write a short, clear, and concise paragraph which explains how the Davisson-Germer experiment shows that electrons are waves. Adapted fromAdapted from

49. Cesium Interferometer Adapted fromAdapted from

50. Interference of BEC Adapted fromAdapted from