608 Appendix: Problem Index
Electron configuration andμfor 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 oflandm 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 2p→ 1 sand 2s− 1 stransitions 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 ofH 2 molecule 2.66
2.2.7 Commutator
To showeipα/xe−ipα/=x+α, Hermicity of operators 2.67
IfAis Hermicity to show thateiAis unitary operator
To distinguish betweeneikxande−ikxand sinaxand cosax 2.68
To show (a) exp(iσxθ)=cosθ+iσxsinθ
(b)(d
dx)†
=−d/dx 2.69
To show (a) [x,px]=ietc (b) [x^2 ,px]= 2 ix 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
[Aˆ,xˆ],[Aˆ,Aˆ],[Aˆ,ˆp]2.74
(a) Eigen value (b) Eigen state (c) Observable 2.75
(a) [x,H]=ip/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)2.78