On separable Schrödinger equations

Abstract

We classify (1+3)-dimensional Schrodinger equations for a particle interacting with the electro-magnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the vector-potentials of the electro-magnetic field A(t; ~x) = (A 0 (t; ~x), ~ A(t; ~x)) providing separability of the corresponding Schrodinger equations