A constant of quantum motion in two dimensions in crossed magnetic and electric fields
arXiv:1006.0326 · doi:10.1088/1751-8113/43/47/474002
Abstract
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial invariant of motion. Do to so we proof that the Hamiltonian is unitarily equivalent to an effective Hamiltonian which commutes with the observable of kinetic energy.
18 pages, 2 figures; the title was changed and several typos corrected; to appear in J. Phys. A: Math. Theor. 43 (2010)