1. Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit of large well depths for the finite square well. The finite square well wavefunctions were computed using an application found at http://webphysics.davidson.edu/faculty/dmb/Single Wells/Well2.html

2. Boundary conditions for infinite barrier:  continuous  can be discontinuous at the barrier edge  under the barrier

3. Note that the y axis only shows units of energy. No units are show for the wavefunction, which is ok since all that matters is that the probability is normalized to unity.

11. Boundary conditions for infinite barrier:  continuous  can be discontinuous at the barrier edge  under the barrier

12. Intuition about the central barrier

23. Boundary conditions for infinite barrier:  continuous  can be discontinuous at the barrier edge  under the barrier

24. Additional discussion about normalizability Key point: There exist “energy eigenstates” for the finite square well with continuous values of the eigenvalue E. These states are only excluded by the requirement that the wavefunction be normalizable.

25. Energy = +36.09

26. Energy = +36.0901

27. Energy = +36.0902

28. Energy = +36.09021

29. Energy = +36.09022

30. Energy = +36.09023

31. Energy = +36.090234

32. Energy = +36.090235

33. Energy = +36.090237

34. Energy = +36.09023772

35. Energy = +36.090237735

36. Energy = +36.0902377385

37. Energy = +36.0902377388

38. Energy = +36.0902377395

39. Energy = +36.0902377399

40. Energy = +36.09023774

41. Energy = +36.09023775

42. Energy = +36.09023776

43. Energy = +36.09023778

44. Energy = +36.0902378

45. Energy = +36.0902379

46. Energy = +36.090238

47. Energy = +36.090239

48. Energy = +36.09024

49. Energy = +36.09025

50. Energy = +36.09026

51. Energy = +36.09029

52. Energy = +36.0904

53. Energy = +36.0907

54. Energy = +36.092

55. Energy = +36.094

56. Energy = +36.097

57. Energy = +36.09

58. Energy = +48

59. Energy = +55

60. Energy = +60

61. Energy = +65

62. Energy = +70

63. Energy = +75

64. Energy = +80

65. Energy = +81.176