Quasi-Stäckel Hamiltonians and Electron Dynamics in an External Field in the Two-Dimensional Case

Abstract

In the two-dimensional case, we construct nondegenerate Hamiltonians that describe electron motion in an electromagnetic field and have additional integrals of motion quadratic in momentum. We completely classify the quasi-Stäckel Hamiltonians related to these systems in the cases where the leading approximation in momenta of the additional integral depends quadratically on the coordinates. We consider reductions of such systems that are symmetric under rotation about the z axis.