Case for group theory as applied to Bloch electrons in a magnetic field

Publisher Website
Google Scholar
Abstract
We have investigated a recent formulation of the problem of a Bloch electron in a uniform magnetic field in which it is predicted that the degeneracy of energy levels is always infinite. This is in direct conflict with the earlier predictions of group theory for the case of "rational" magnetic fields. It is shown that, if the new theory is correct, it implies the existence of additional invariance properties of the Hamiltonian over and above that corresponding to the magnetic translation group. This implies group theory is still applicable, but with a larger group. However, evidence is given that the conclusion of infinite degeneracy does not hold and that the earlier theory is correct. It is also shown that the use of rational fields, like that of periodic boundary conditions, is a convenience and does not unduly restrict the applicability of the theory.