Phys 4910 - Spectroscopy Assignment 6
due Wednesday March 21st 2018


Assignment

  1. For the hydrogen atom the energy only depends on the principal quantum number (n). However the wavefunction depends on n, l, ml, and ms. That means that there are multiple wavefunctions (each one comprising a given state) which correspond to the same energy, a condition known as degeneracy.
    1. Show that for a given value of the orbital quantum number (l) there are 2(2l+1) degenerate states
    2. Show that for a given value of n there are 2n2 degenerate states.
  2. For each of the configurations below give the total degeneracy
    1. 2s 2p
    2. 2s 3d
    3. 2p 4d
    4. 3d 4f 5g
  3. 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.
    1. 1s 2p
    2. 2p 3d
    3. 3d 5g