Quasiseparation of variables in the Schroedinger equation with a magnetic field

Abstract

We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the separation of variables in the Schroedinger equation. We introduce the concept of "quasiseparation of variables" and show that in many cases it allows us to reduce the calculation of the energy spectrum and wave functions to linear algebra.