Magnetic Translation Group. II. Irreducible Representations

The physical irreducible representations of the magnetic translation group (M. T. G. ) defined previously have been found. From these a set of solutions of Schr\"odinger's equation for a Bloch electron in a magnetic field has been constructed. In general the M. T. G. is non-Abelian. However, when the magnetic flux through areas enclosed by any vectors of the Bravais lattice become multiples of an elementary "fluxon" hce, the M. T. G. becomes isomorphic to the usual translation group.