Appendix: Problem Index 611
3.2.5 Hydrogen Atom
Expectation value of U and E 3.64
Maximum electron density and mean radius 3.65
To show that 3d functions are orthogonal to each other 3.67
Degree of degeneracy forn=1, 2, 3, 4 3.68
Parity of 1s,2p,3dstates 3.69
To show that 3dfunctions are spherically symmetric 3.70
Probability for electron to lie within a sphere of radiusR 3.71, 76
Maximum and minimum electrons density in 2sorbit 3.72
In the phosphorous mesic atom photon wavelength in the transition
3 d→ 2 pis calculated and lifetime in the 3dstate estimated 3.73
Momentum probability distribution of electron 3.74
Most probable momentum and mean value of electron 3.75
3.2.6 Angular Momentum
[Lx,Ly]=iLz 3.77
Eigen value ofS 1 .S 2 3.78
σp.σn=−3 for singlet state and=1 for triplet state 3.79
Lz=−i∂φ∂ 3.80
Expressions forLxandLyin spherical polar coordinates 3.81
[L^2 ,Lx]=0 etc 3.82
Expression forL^2 /(i)^2 in spherical polar coordinates 3.83
Angular momentum matrices forj= 1 /2 andj^2 3.84
Angular momentum matrices forj=1 andj^2 3.85
Clebsch-Gordon coefficients forj 1 =1 andj 2 = 1 /23.86
For given wavefunction to show the probability is zero forl= 0
andl=1, and is unity forl= 23.87
To show that a set of wavefunctions belong toLzand to obtain
eigen values3.88
For given stationary state wavefunction to findLzandL^2 3.89
Given a wavefunction for H-atom to findLzand parity 3.90
To applyL+andL−to 2peigen functions of H-atom 3.91
Nuclear spin from rotational spectra of diatomic molecules 3.92
To re-express given angular wave function as combination of
spherical harmonics3.93
Given a wavefunction of a hydrogen-like atom, to findLz 3.94
Given the wavefunction for a state, to get values ofLzand to find
the corresponding probabilities3.95
To prove commutation rules involvingJx,Jy,JzandJ+ 3.96
3.2.7 Approximate Methods
To calculate correction to the potential of hydrogen atom 3.97
Stationary energy levels of a charged particle oscillating with a
given frequency in an electric field3.98
To work out the perturbed levels 3.99
To find the ionization energy of helium atom by variation method 3.100