4. Good Evening to all of YOU!

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

6. Outline 1. Wave or Particle?..Two slit experiments 2. Uncertainty Principle 3. Standing Waves 4. Stationary States - Atomic Orbitals 5. Do we understand Quantum Mechanics? 6. The Path Integral – Random Walk 7. The Copenhagen Interpretation 8. The Schroedinger’s Cat 9. The EPR Paradox

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

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

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

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

11. http://www.hqrd.hitachi.co.jp/em/doubleslit.cfm 1/1000 mm

13. God does not play dice! This type of behavior was observed first in the case of light!

14. Newton Light is a beam of particles Compton In my scattering expts, light - beam of particles Huygens Exhibits interference, hence waves! Einstein In photoelectric effect, light behaves like particles Maxwell EM Theory, hence waves History

15. It is both! It has a DUAL NATURE On Mondays, Wednesdays and Fridays, it is a PARTICLE! On, Tuesdays,Thursdays and Saturdays it is a WAVE! Not only electrons and photons,but EVERYTHING has this dual nature! Exptly shown for protons, neutrons, He atoms, even C 60 ! Oh LORD, please, is it a PARTICLE or a WAVE!!??? On Sundays

16. Prof. A. Zeilinger http://www.quantum.univie.ac.at/zeilinger/ C 60

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

18. De Broglie - Heisenberg de Broglie Heisenberg

19. Reflection

21. Modes of a String - Standing waves

26. Standing waves of a bridge

27. On a rectangular membrane Stretched membrane Time dependent wave

31. Stretched membrane No nodes Two nodes Four nodes One node Infinite modes One node

33. Particle in a box Box Standing wave patterns in 2D can be formed!

34. From work of Eigler (IBM)

37. + - Hydrogen Atom: e - bound to proton Box Standing wave patterns in 3D can be formed!

38. d xy dz2dz2 fz3fz3 gz4gz4 pzpz Atomic Orbitals Standing waves in 3 dimensions

39. Electron density goes into internuclear region! Constructive interference! Electron density goes away from the internuclear region! Destructive interference! leads to bonding

40. How does it know that both the slits are open!!?? Do we understand Quantum Mechanics? I don’t understand it!! Nobody does!!! At least this time, he is sensible!

41. Does it go through both the slits?

42. How does an electron move (propagate)? Through all possible paths! He is crazy!

43. More slits Even more Complex setup Source of particles

44. In the limit of  walls each with  slits……. All paths contribute! Action

45. Quantum mechanics and the drunken walker

46. Haddock in the Evening BAR We can only talk of Probabilities!

47. Some paths are more probable than others BAR

48. I have always known that the electron is weird!

49. 1. G. Gamov, Tompkins in Paperback, Canto Books. CUP, 1993 2. R.Gilmore, Alice in Quantum Land, Affiliated East West Press Ltd. 1994 3. Gribbin, Schrodinger’s Cat, Black Swan, London, 1984 4. Cropper, The Quantum Physicists, OUP, 1971 5. J. Gribbin, Schrodinger’s Kittens, Little, Brown & Co. London, 1995 6. G. Gamov and R. Stannard, The New World of Tompkins, Cambridge Univ. Press, 1999 7. R.P. Feynamn, QED, Princeton University Press, 1988 8. R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill, New York, 1965. REFERENCES

50. See: www.colorado.edu/physics2000 I think it is safe to say that no one understands quantum mechanics. Richard Feynman The reason universities have students is so they can teach the professors, and Feynman was one of the best (students). John Wheeler

51. What do you think of Quantum Mechanics? OR