On a Degeneracy Theorem of Kramers

There is a theorem due to Kramers which states that the energy states of systems with an odd number of electrons remain at least doubly degenerate in the presence of any purely electric fields. The physical significance of this theorem, its proof, and a discussion of the relationship of the Kramers degeneracy and the Wigner time-reversal operation are considered. A proof is given of the theorem that the expectation value of the magnetic moment operator is zero for any nondegenerate state.