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Abstract <p>The discrete Shchrödinger operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(h(k)\)</EquationSource> <!--LobJMat2460809Muminov-m1--> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="128" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\in\mathbb{T}^{3}=(-\pi,\pi]^{3}\)</EquationSource> <!--LobJMat2460809Muminov-m2--> </InlineEquation>, corresponding to a two-fermion system interacting with first and second nearest-neighboring-site interactions of magnitudes <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda,\mu\in\mathbb{R}_{+}\)</EquationSource> <!--LobJMat2460809Muminov-m3--> </InlineEquation> on the three dimensional lattice is considered. Conditions for the existence of eigenvalues of the two-particle Schrödinger operator <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(h(k)\)</EquationSource> <!--LobJMat2460809Muminov-m4--> </InlineEquation> are found for any <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\in\mathbb{T}^{3}\)</EquationSource> <!--LobJMat2460809Muminov-m5--> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8174_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda,\mu\in\mathbb{R}_{+}\)</EquationSource> <!--LobJMat2460809Muminov-m6--> </InlineEquation>.</p>

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Spectral Properties of the Hamiltonian of a Two-Fermion System

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • M. I. Muminov,
  • A. M. Khurramov

摘要

Abstract

The discrete Shchrödinger operator \(h(k)\) , \(k\in\mathbb{T}^{3}=(-\pi,\pi]^{3}\) , corresponding to a two-fermion system interacting with first and second nearest-neighboring-site interactions of magnitudes \(\lambda,\mu\in\mathbb{R}_{+}\) on the three dimensional lattice is considered. Conditions for the existence of eigenvalues of the two-particle Schrödinger operator \(h(k)\) are found for any \(k\in\mathbb{T}^{3}\) and \(\lambda,\mu\in\mathbb{R}_{+}\) .