  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.
