Energy Levels of Conduction Electrons in a Magnetic Field

The energy levels of an electron in a periodic potential and a constant magnetic field are found as the solutions to a secular determinant when the following approximations are made: (a) the energy band of interest is spherically symmetric and (b) lattice broadening of the levels is neglected. Inclusion of spin-orbit coupling gives the $g$ factor as function of position in the band. Perturbation theory is used to treat the effect on the free energy of small departures of the band from spherical symmetry.