Phys 4910  Spectroscopy Assignment 6
due Wednesday March 21^{st} 2018
Assignment

For the hydrogen atom the energy only depends on the principal quantum
number (n). However the wavefunction depends on n, l, m_{l}, and
m_{s}. That means that there are multiple wavefunctions (each one
comprising a given state) which correspond to the same energy, a condition
known as degeneracy.

Show that for a given value of the orbital quantum number (l) there are
2(2l+1) degenerate states

Show that for a given value of n there are 2n^{2} degenerate states.

For each of the configurations below give the total degeneracy

2s 2p

2s 3d

2p 4d

3d 4f 5g

For each of the following configurations determine the possible terms which
can arise. For each one calculate the degeneracy, and show that the sum
of the degeneracies of the term is equal to the degeneracy of the configuration.

1s 2p

2p 3d

3d 5g