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Abstract <p>In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8172_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(h_{\mu}\)</EquationSource> <!--LobJMat2460810Kuljanov-m1--> </InlineEquation> depending on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8172_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu\)</EquationSource> <!--LobJMat2460810Kuljanov-m2--> </InlineEquation> is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8172_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(h_{\mu}\)</EquationSource> <!--LobJMat2460810Kuljanov-m3--> </InlineEquation> is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found.</p>

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On the Spectrum of the Two-Particle Schrödinger Operator with Point Potential: Two Dimensional Case

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • U. N. Kuljanov

摘要

Abstract

In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) \(h_{\mu}\) depending on \(\mu\) is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of \(h_{\mu}\) is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found.