Bound state solutions of the two--dimensional Schr\"{o}dinger equation with Kratzer--type potentials

• URL: http://arxiv.org/abs/2311.02694v2
• Date: Mon, 20 Nov 2023 03:45:09 GMT
• Title: Bound state solutions of the two--dimensional Schr\"{o}dinger equation with Kratzer--type potentials
• Authors: Roman Ya. Kezerashvili, Jianning Luo, and Claudio R. Malvino
• Abstract summary: The Schr"odinger 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 Schr"odinger equation with Kratzer-type potentials.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger 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 Schr\"{o}dinger 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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