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<p>Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schrödinger equation is applied for a solution of a two–dimensional (2D) problem for two particles interacting via Kratzer, and modified Kratzer potentials. We found the exact bound state solutions of the two–dimensional Schrödinger equation with Kratzer–type potentials and present analytical expressions for the eigenvalues and eigenfunctions. The eigenfunctions are given in terms of the associated Laguerre polynomials. The analytical expressions for the eigenvalues and eigenfunctions obtained by using the standard method could be beneficial in various physical analyses, including the chemical dissociation energy of the lowest vibrational level and equilibrium internuclear separation of the diatomic molecule, and retrieval of the material parameters such as reduced exciton mass and screening length from measured exciton energies. We also report analytical expressions for expectation values for <i>r</i> and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6150_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(r^2\)</EquationSource> </InlineEquation>, and the range of strength parameter <i>g</i> for modified Kratzer potential for excitons in freestanding transition metal dichalcogenides that reproduce theoretical and experimental binding energies.</p>

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Kratzer and Modified Kratzer Potentials in Two Dimensions: Exact Solutions and Exciton Applications

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Roman Ya. Kezerashvili,
  • Jianning Luo,
  • Claudio R. Malvino,
  • Anastasia Spiridonova

摘要

Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schrödinger equation is applied for a solution of a two–dimensional (2D) problem for two particles interacting via Kratzer, and modified Kratzer potentials. We found the exact bound state solutions of the two–dimensional Schrödinger equation with Kratzer–type potentials and present analytical expressions for the eigenvalues and eigenfunctions. The eigenfunctions are given in terms of the associated Laguerre polynomials. The analytical expressions for the eigenvalues and eigenfunctions obtained by using the standard method could be beneficial in various physical analyses, including the chemical dissociation energy of the lowest vibrational level and equilibrium internuclear separation of the diatomic molecule, and retrieval of the material parameters such as reduced exciton mass and screening length from measured exciton energies. We also report analytical expressions for expectation values for r and \(r^2\) , and the range of strength parameter g for modified Kratzer potential for excitons in freestanding transition metal dichalcogenides that reproduce theoretical and experimental binding energies.