A. V. Pereskokov, “Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels”, TMF, 2025, Volume 222, Number 3,Pages <nobr>531

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

A. V. Pereskokov^ab

^a National Research University ``Moscow Power Engineering Institute,'' Moscow, Russia
^b National Research University ``Higher School of Economics,'' Moscow, Russia

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.

Keywords: hypergeometric coherent states, coherent transformation, self-consistent field, asymptotic eigenvalue, asymptotic eigenfunction, saddle-point method.

Received: 22.08.2024
Revised: 29.09.2024

DOI: 10.4213/tmf10811