1. Chapter 2 The Schrodinger Equation

2.  wave function of a free particle.  Time dependent Schrodinger equation.  The probability density.  Expectation values for momentum and energy.  Operators.  Relation between expectation values and operators. 2

3. Wave equation Dr. Maha Torjman 3

4. Classical Wave equation Dr. Maha Torjman 4

5. Schrödinger Wave equation Dr. Maha Torjman 5

6. 6

7. wave function for a free particle. Dr. Maha Torjman E 0 = 0 from the relativistic Particle 7

8. wave function for a free particle Dr. Maha Torjman 8

9. 9

10. 10

11. Dr. Maha Torjman 11

12. 12

13. Dr. Maha Torjman 13

14. Momentum and Energy operators Dr. Maha Torjman 14

15. Dr. Maha Torjman 15

16. ( Example using operators ) 16

17. Dr. Maha Torjman 17

18. 18

19. Expectation Value 19

20. 20

21. 21

22. 22

23. Dr. Maha Torjman 23

24. 24

25. 25

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27. 27

28. Expectation Values Dr. Maha Torjman 28

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30. Dr. Maha Torjman 30

31. 31

32. Dr. Maha Torjman 32

33. Expectation value and operators Dr. Maha Torjman 33

34. Dr. Maha Torjman 34

35. Dr. Maha Torjman 35

36. Time-independent Schrodinger equation(1) Dr. Maha Torjman 36

37. Time-independent Schrodinger equation(2) Dr. Maha Torjman 37

38. Time-independent Schrodinger equation(3) Dr. Maha Torjman 38

39. Time-independent Schrodinger equation(4) 39

40. Required properties of eigenfunctions Dr. Maha Torjman 40

41. Dr. Maha Torjman 41

42. 42

43. Dr. Maha Torjman 43

44. Example ( standard deviation ) 44

45. Dr. Maha Torjman 45

46. Summary(2) Dr. Maha Torjman 46

47. Homework 47