  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.
