INVARIANCE GROUPS OF SCHROEDINGER EQUATION FOR CASE OF UNIFORM MAGNETIC FIELD .I.

This paper is an extension of the group theory treatment of the Schroedinger equation of an electron in the presence of an electrostatic, periodic field and a uniform magnetic field, as given by Brown and by Zak. The invariance groups for this case are defined and studied for an arbitrary gauge. In particular, the properties of the invariance translation operator groups and their irreducible representations are considered in detail for all possible orientations and magnitudes of the magnetic field. It turns out that for most orientations and magnitudes of the magnetic field only infinite dimensional representations have a physical meaning. Basis functions generating both finite and infinite dimensional representations are constructed from the eigenfunctions of the Schroedinger equation in the absence of the electrostatic field. Some implications this has for the selection rules for the matrix elements of the electrostatic potential are also discussed. © 1969.