标题： 二维薛定谔方程与克雷茨类型势能的束缚态解 显示英文标题

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

摘要： 精确可解模型在量子物理的许多领域中起着极其重要的作用。 在本研究中，薛定谔方程被用于求解两个粒子通过Kratzer和修改的Kratzer势相互作用的二维（2D）问题。 我们找到了带有Kratzer型势的二维薛定谔方程的精确束缚态解，并给出了特征值和特征函数的解析表达式。 特征函数以关联的拉盖尔多项式的形式给出。 显示英文摘要

摘要： 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.