Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field, perturbed by a decreasing electric field. I (Q1101881)

One investigates the bound states \(E_ n\), situated to the left of the boundary of the continuous spectrum. Under the assumption that the potential is nonpositive and has at infinity a power type asymptotics, one computes the principal term of the asymptotics \(E_ n\) as \(n\to \infty\). One does not assume the axial symmetry of the potential of the electric field.