Download presentation

Presentation is loading. Please wait.

Published byMarcelo Lemmon Modified over 2 years ago

1
I.What to recall about motion in a central potential II.Example and solution of the radial equation for a particle trapped within radius “a” III.The spherical square well (Re-)Read Chapter 12 Section 12.3 and 12.4 1

2
Ignore center of mass motion Focus on this “H μ ” m1m1 m2m2 O 2

3
the angular momentum operator 3

4
4

5
5

6
6 Normalization not yet specified Spherical Neuman function, Irregular @ r=0, so get D=0

7
7 I.Particle in 3-D spherical well (continued) II.Energies of a particle in a finite spherical well Read Chapter 13

8
8 In spectroscopy the rows are labelled by:

9
9

10
10 I. Energies of a particle in a finite spherical square well

11
11 V(r) a 0 -V 0 r I II 0

12
12 V(r) a 0 -V 0 r I II 0 0 +V 0

13
13

14
14

15
15 y 0π/2π3π/2 2π5π/2 3π7π/24π LHS(-cot)

16
16 y 0π/2π3π/2 2π5π/2 3π7π/24π How the value of λ affects the plot: y1y1 y2y2 y3y3

17
17 V(r) a 0 -V 0 r I II 0

18
18 To solve this define: and Then the radial equation becomes: The solution is:

19
19 I.Energies of a particle in a finite spherical square well, continued II.The Hydrogen Atom

20
20

21
21

22
22 I.Energies of a particle in a finite spherical square well (continued) II.The Hydrogen Atom

23
23

24
24 # protons in nucleus Charge of electron energy levels

25
25 Defined as E<0

26
26

27
27 solution

28
28 I.The Hydrogen Atom (continued) II.Facts about the principal quantum number n III.The wavefunction of an e - in hydrogen

29
29

30
30

31
31

32
32

33
33

34
34 I.Facts about the principal quantum number n (continued) II.The wavefunction of an e - in hydrogen III.Probability current for an e - in hydrogen

35
35

36
36

37
37 Normalization not determined yet

38
38

39
39 I.Facts about Ψ e in hydrogen II.Probability current for an e - in hydrogen Read 2 handouts Read Chapter 14

40
40

41
41 E>0 (scattering) states (we will study these in Chapter 23) E<0 (bound) states

42
42 etc. 2p 2s 3p 3s The n=1 shell The n=2 shell The n=3 shell

43
43

44
44 Review Syllabus Read Goswami section 13.3 and chapter 14 plus the preceding chapter as necessary for reference

45
45 Read Chapter 14 I.Probability current for an e - in hydrogen II.The effect of an EM field on the eigen functions and eigen values of a charged particle III.The Hamiltonian for the combined system of a charged particle in a general EM field

46
46

47
47

48
48 A O

49
49 angular momentum operator magnetic momentum operator quantum number “m” This factor is called the Bohr magneton Magnitude of the z- component of magnetic dipole moment of the e -

50
50 I.The effect of an EM field on the eigen functions and eigen values of a charged particle II.The Hamiltonian for the combined system of a charged particle in a general EM field III.The Hamiltonian for a charged particle in a uniform, static B field Read Chapter 15

51
51

52
52 I.The Hamiltonian for a charged particle in an EM field II.The Hamiltonian for a charged particle in a uniform, static B field III.The normal Zeeman effect

53
53

54
54

55
55

56
56

57
57 O

58
58

59
59

60
60

61
61

62
62

63
63

64
64

65
65 E

66
66 Set = 0 for now H 2D, HO

67
67

68
68

69
69

70
70

71
71

72
72

73
73

74
74

75
75

76
76

77
77

78
78

79
79

80
80

81
81

82
82

83
83

84
84

85
85

86
86

87
87

88
88

89
89

90
90

91
91

92
92

93
93

94
94

95
95

96
96

97
97

98
98

99
99

100
100

Similar presentations

OK

Bohr Model. Hydrogen Model A hydrogen atom is a single electron and proton. One negative charge One positive charge Assume that the discrete energies.

Bohr Model. Hydrogen Model A hydrogen atom is a single electron and proton. One negative charge One positive charge Assume that the discrete energies.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on water activity Ppt on pin photodiode Ppt on security attacks in information security Ppt on nuclear family and joint family history Ppt on story of taj mahal Ppt on electrical power generation system using railway track slides Ppt on bluetooth broadcasting system Ppt on history of olympics rings A ppt on right to education Ppt on area of trapezium example