Question

Consider an electron bound in a three dimensional simple harmonic oscillator potential in the n=1 state. Recall that the e^- has spin 1/2 and that the n=1 level of the oscillator has l =1. Thus, there are six states {|n=1, l=1, m_l, m_s} with m_l= +1, 0, -1 and m_s = +/- 1/2.

- Using these states as a basis find the six states with definite j and m_j where J = L +s

- What are the energy levels in the presence of a spin-orbit interaction AL.s where A is the strength of the interaction. What are the degeneracies?

- If now a weak magnetic field B₀ is applied along the z-axis how will it affect the degeneracy of the J=1/2 level?

Answer 1