1. V6543210V6543210

2. V6543210V6543210

3. The wavefunctions of the Simple Harmonic Oscillator are Orthonormal

4. Orthonormal wavefunctions

5. ∫ + ∞ - ∞ ψ v ” ψ v ’ dτ = δ v ” v ’ Orthonormal wavefunctions

6. ∫ + ∞ - ∞ ψ v ” ψ v ’ dτ = δ v ” v ’ Orthonormal wavefunctions Kronecker delta δ ij = 1 when i = j and 0 when i ≠ j

7. + + ∫ + ∞ - ∞ ψ v=0 ψ v =0 dτ = 0 Orthonormal wavefunctions ← – ∞ + ∞ →

8. V6543210V6543210

9. + – ∫ + ∞ - ∞ ψ v=1 ψ v =0 dτ = 0 Orthonormal wavefunctions ← – ∞ + ∞ →

10. V6543210V6543210

11. + + – ∫ + ∞ - ∞ ψ v=2 ψ v =0 dτ = 0 Orthogonal wavefunctions ← – ∞ + ∞ →

12. Anharmonic oscillator wavefunctions and probabilities

19. V6543210V6543210

21. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

23. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

24. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

25. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

26. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

27. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

28. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

29. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

30. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

31. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

32. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

34. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

35. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

36. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

37. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

38. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

39. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

40. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

41. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

42. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

43. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

44. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

45. x → -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

46. x → ↑y↑y -8 -6 -4 -2 0 2 4 6 8 12 10 8 6 4 2 0 y = x 2

47. http://en.wikipedia.org/wiki/File:Simple_harmonic_oscillator.gif

48. H + H E(r) r  0 Rotational levels Continuum wavefunction of a dissociating state

49. http://131.104.156.23/Lectures/CHEM_207/uv-vis.htm

51. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html

57. H + H r  E(r) The problem of how to make H 2 in Space H2H2

62. http://jchemed.chem.wisc.edu/JCEDLib/SymMath/collection/article.php?id=29

63. http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_III/Molekuelschwingungen.htm