On some integrable cases of the two-dimensional motion of a charged particle in an electromagnetic field

Two cases of the two-dimensional motion of a charged particle in an electromagnetic field have been integrated. In these cases, the Hamiltonian commutes with the angular momentum. Variables are separable in polar coordinates. The vector potential and potential energy have been taken from my recent work regarding two cases of the two-dimensional Schrödinger equation, which belong to quasi-exactly solvable problems. In these cases, semiclassical and exact wavefunctions have been compared in classically forbidden regions.