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 for n = 1, 2, 3, 4
3.68
Parity of 1s, 2p, 3d states
3.69
To show that 3d functions are spherically symmetric
3.70
Probability for electron to lie within a sphere of radius R
3.71, 76
Maximum and minimum electrons density in 2s orbit
3.72
In the phosphorous mesic atom photon wavelength in the transition
3d → 2p is calculated and lifetime in the 3d state 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
[L x , L y ] = iL z
3.77
Eigen value of S 1 .S 2
3.78
σ p .σ n = −3 for singlet state and = 1 for triplet state
3.79
L z = −i
∂
∂ϕ
3.80
Expressions for L x and L y in spherical polar coordinates
3.81
[L
2
, L x ] = 0 etc
3.82
Expression for L
2
/(i)
2 in spherical polar coordinates
3.83
Angular momentum matrices for j = 1/2 and j
2
3.84
Angular momentum matrices for j = 1 and j
2
3.85
Clebsch-Gordon coefficients for j 1 = 1 and j 2 = 1/2
3 . 8 6
For given wavefunction to show the probability is zero for l = 0
and l = 1, and is unity for l = 2
3.87
To show that a set of wavefunctions belong to L z and to obtain
eigen values
3.88
For given stationary state wavefunction to find L z and L
2
3.89
Given a wavefunction for H-atom to find L z and parity
3.90
To apply L + and L − to 2p eigen 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 harmonics
3.93
Given a wavefunction of a hydrogen-like atom, to find L z
3.94
Given the wavefunction for a state, to get values of L z and to find
the corresponding probabilities
3.95
To prove commutation rules involving J x , J y , J z and J +
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 field
3.98
To work out the perturbed levels
3.99
To find the ionization energy of helium atom by variation method
3.100
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 for n = 1, 2, 3, 4
3.68
Parity of 1s, 2p, 3d states
3.69
To show that 3d functions are spherically symmetric
3.70
Probability for electron to lie within a sphere of radius R
3.71, 76
Maximum and minimum electrons density in 2s orbit
3.72
In the phosphorous mesic atom photon wavelength in the transition
3d → 2p is calculated and lifetime in the 3d state 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
[L x , L y ] = iL z
3.77
Eigen value of S 1 .S 2
3.78
σ p .σ n = −3 for singlet state and = 1 for triplet state
3.79
L z = −i
∂
∂ϕ
3.80
Expressions for L x and L y in spherical polar coordinates
3.81
[L
2
, L x ] = 0 etc
3.82
Expression for L
2
/(i)
2 in spherical polar coordinates
3.83
Angular momentum matrices for j = 1/2 and j
2
3.84
Angular momentum matrices for j = 1 and j
2
3.85
Clebsch-Gordon coefficients for j 1 = 1 and j 2 = 1/2
3 . 8 6
For given wavefunction to show the probability is zero for l = 0
and l = 1, and is unity for l = 2
3.87
To show that a set of wavefunctions belong to L z and to obtain
eigen values
3.88
For given stationary state wavefunction to find L z and L
2
3.89
Given a wavefunction for H-atom to find L z and parity
3.90
To apply L + and L − to 2p eigen 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 harmonics
3.93
Given a wavefunction of a hydrogen-like atom, to find L z
3.94
Given the wavefunction for a state, to get values of L z and to find
the corresponding probabilities
3.95
To prove commutation rules involving J x , J y , J z and J +
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 field
3.98
To work out the perturbed levels
3.99
To find the ionization energy of helium atom by variation method
3.100