Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels

Abstract

The spectral problem for the hydrogen atom in a magnetic field perturbed by a self-consistent field is considered. An asymptotic expansion of self-consistent energy levels is obtained. An asymptotic expansion of hypergeometric coherent states near the sphere \(|q|=2\) is found. The asymptotics of the norm of the asymptotic eigenfunctions in the space \(L^2(\mathbb{R}^3)\) is calculated.