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Abstract <p> 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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2608_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(|q|=2\)</EquationSource> </InlineEquation> is found. The asymptotics of the norm of the asymptotic eigenfunctions in the space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2608_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2(\mathbb{R}^3)\)</EquationSource> </InlineEquation> is calculated. </p>

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

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • A. V. Pereskokov

摘要

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.