Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields

Abstract

In the presence of the homogeneous electric field [Formula: see text] and the homogeneous perpendicular magnetic field [Formula: see text], the classical trajectory of a quantum particle on [Formula: see text] moves with drift velocity [Formula: see text] which is perpendicular to the electric and magnetic fields. For such Hamiltonians, the absence of the embedded eigenvalues of perturbed Hamiltonian has been conjectured. In this paper, one proves this conjecture for the perturbations [Formula: see text] which have sufficiently small support in the direction of drift velocity.