Bound state solutions of the two--dimensional Schrödinger equation with Kratzer--type potentials

2023/11/05 by Roman Ya. Kezerashvili, Kezerashvili, Roman Ya., Jianning Luo +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2311.02694

openalex publication_date 2023/11/05 · openalex created_date 2023/11/08 · openalex updated_date 2026/07/28

Abstract

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.

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