Kratzer-type potentials in two dimensions: exact solutions and applications

ORAL

Abstract

We report the exact bound-state solutions of the two-dimensional Schrödinger equation with Kratzer-type potentials and derive analytical expressions for the corresponding eigenvalues and eigenfunctions [1]. Analytical formulas are also obtained for the expectation values for r and r2, and the range of strength parameter g for the modified Kratzer potential for excitons in freestanding transition metal dichalcogenides that reproduce theoretical and experimental binding energies. These results 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.

[1] R.Ya. Kezerashvili, J. Luo, C.R. Malvino, A. Spiridonova, Kratzer and Modified Kratzer Potentials in Two Dimensions: Exact Solutions and Exciton Applications, Int. J. Theor. Phys. 64, 278 (2025).

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Publication: R.Ya. Kezerashvili, J. Luo, C.R. Malvino, A. Spiridonova, Kratzer and Modified Kratzer Potentials in Two Dimensions: Exact Solutions and Exciton Applications, Int. J. Theor. Phys. 64, 278 (2025).

Presenters

  • Roman Ya Kezerashvili

    • The Graduate Center, City University of New York

Authors

  • Roman Ya Kezerashvili

    • The Graduate Center, City University of New York

  • Jianning Luo

    • New York City College of Technology, City University of New York

  • Claudio R Malvino

    • New York City College of Technology, City University of New York

  • Anastasia Spiridonova

    • 1New York City College of Technology, The City University of New York, USA