A transformation method of generating exact analytic solutions of the Schrodinger equation

A transformation method is presented which consists of a coordinate transformation and a functional transformation that allow generation of normalized exact analytic bound-state solutions of the Schrodinger equation, starting from an analytically solved quantum problem. The coordinate transformation is the basic transformation, which is supplemented by the functional transformation so that one can choose the dimension of the space of the transformed system. By repeated application of the method, it is possible to generate a number of solved quantum problems in the case that the original quantum system has a multiterm potential. It is shown that the eigenfunction of the transformed system can be easily normalized in most cases.