608
Appendix: Problem Index
Electron configuration and μ for H and Na
2.39
Magnetic moment, Stern–Gerlah’s experiment
2.40
Transition element, rare-earth element, electronic structure
2.41
Bohr magneton
2.44
2.2.5 Spectroscopy
Allowed values of l and m
2.45
Forbidden transitions in dipole transitions
2.46
Hyperfine quantum number for
9 Be
+
2.47
Doppler line width temperature broadening
2.48
Zeeman effect in weak field in alkali atom
2.49
Calcium triplet-Fine structure
2.50
Zeeman effect in Sun spot
2.51
Normal Zeeman effect
2.52
Sketch for Zeeman splitting
2.53
Energy levels of mercury spectrum
2.54
Life times of 2 p → 1s and 2s − 1s transitions
2.55
Population of states in Helium-Neon laser
2.56
2.2.6 Molecules
Modes of motion of a diatomic molecule
2.57
Rotational spectral lines in H-D molecule
2.58
Alternate intensities of rotational spectrum
2.59
Excited state of CO molecule
2.60
Boltzman distribution of rotational states
2.61
Vibrational states of NO molecule
2.62
Rotational states of CO molecule
2.63
H 2 molecule as a rigid molecule
2.64
Mass number of unknown carbon isotope
2.65
Force constant of H 2 molecule
2.66
2.2.7 Commutator
To show e
i pα/ xe
−i pα/
= x + α, Hermicity of operators
2.67
If A is Hermicity to show that e
i A is unitary operator
To distinguish between e
ikx and e
−ikx and sin ax and cos ax
2.68
To show (a) exp(iσ xθ) = cos θ + iσ x sin θ
(b)
d
dx
† = −d/dx
2.69
To show (a) [x, p x ] = i etc (b) [x
2
, p x ] = 2ix
2.70
Linearity of hermitian operator
2.71
Hermicity of momentum operator
2.72
Necessary condition for commuting operators
2.73
(a) Hermitian adjoint operator (b) Commutators
[ ˆ
A, ˆ
x], [ ˆ
A, ˆ
A], [ ˆ
A, ˆ
p]
2.74
(a) Eigen value (b) Eigen state (c) Observable
2.75
(a) [x, H ] = i p/μ (b) [[x, H ], x] =
2
/μ
2.76
[A
2
, B] = A[A, B] + [A, B]A
2.77
(σ. A)(σ.B) = A · B + iσ · ( A × B)
2 . 7 8
Appendix: Problem Index
Electron configuration and μ for H and Na
2.39
Magnetic moment, Stern–Gerlah’s experiment
2.40
Transition element, rare-earth element, electronic structure
2.41
Bohr magneton
2.44
2.2.5 Spectroscopy
Allowed values of l and m
2.45
Forbidden transitions in dipole transitions
2.46
Hyperfine quantum number for
9 Be
+
2.47
Doppler line width temperature broadening
2.48
Zeeman effect in weak field in alkali atom
2.49
Calcium triplet-Fine structure
2.50
Zeeman effect in Sun spot
2.51
Normal Zeeman effect
2.52
Sketch for Zeeman splitting
2.53
Energy levels of mercury spectrum
2.54
Life times of 2 p → 1s and 2s − 1s transitions
2.55
Population of states in Helium-Neon laser
2.56
2.2.6 Molecules
Modes of motion of a diatomic molecule
2.57
Rotational spectral lines in H-D molecule
2.58
Alternate intensities of rotational spectrum
2.59
Excited state of CO molecule
2.60
Boltzman distribution of rotational states
2.61
Vibrational states of NO molecule
2.62
Rotational states of CO molecule
2.63
H 2 molecule as a rigid molecule
2.64
Mass number of unknown carbon isotope
2.65
Force constant of H 2 molecule
2.66
2.2.7 Commutator
To show e
i pα/ xe
−i pα/
= x + α, Hermicity of operators
2.67
If A is Hermicity to show that e
i A is unitary operator
To distinguish between e
ikx and e
−ikx and sin ax and cos ax
2.68
To show (a) exp(iσ xθ) = cos θ + iσ x sin θ
(b)
d
dx
† = −d/dx
2.69
To show (a) [x, p x ] = i etc (b) [x
2
, p x ] = 2ix
2.70
Linearity of hermitian operator
2.71
Hermicity of momentum operator
2.72
Necessary condition for commuting operators
2.73
(a) Hermitian adjoint operator (b) Commutators
[ ˆ
A, ˆ
x], [ ˆ
A, ˆ
A], [ ˆ
A, ˆ
p]
2.74
(a) Eigen value (b) Eigen state (c) Observable
2.75
(a) [x, H ] = i p/μ (b) [[x, H ], x] =
2
/μ
2.76
[A
2
, B] = A[A, B] + [A, B]A
2.77
(σ. A)(σ.B) = A · B + iσ · ( A × B)
2 . 7 8