BLOCH ELECTRONS IN A MAGNETIC FIELD-REDUCTION TO ONE DIMENSION

A reduction to one dimension of the above problem, found by Schellnhuber and Obermair for a special model lattice, is shown to be valid for all lattices without restriction. As was the case in their problem, the field must be rational. If the rational number is the reciprocal of an integer a single equation results. This condition is well adapted to the study of fields of practically attainable magnitude. If the rational number is of the form q/p a system of q coupled equations is obtained. © 1980 American Institute of Physics.