A theorem due to Wannier for treating the motion of electrons in a perturbed periodic field is generalized to include the effect of a slowly varying magnetic field. It is shown that the problem reduces to that of solving an effective Schrödinger equation, which is known as soon as we have solved the problem without perturbing fields.

• Received 25 June 1951

DOI:https://doi.org/10.1103/PhysRev.84.814