Effects of Magnetic field applied to Hydrogen-like atom.

[cwatson]

1. Apply a magnetic field B to a hydrogen like atom. This gives rise to an additional potential energy term of mu_b*B*L_z/hbar

a) Show that the eigenfunction PSI_nlm is still an eigenfunction in the presence of the magnetic field

b) Show that the eigenvalues are E_n + m*mu_b*B


How do you show that the eigenfunction remains?

 

[Matterwave]

What's the usual Eigenfunction equation? (Hint, it is Schroedinger's equation), how has that changed with this added potential energy term?

Alternatively, does this new Hamiltonian commute with the old one? What do commuting operators have in common?