ABSTRACT
In this chapter we discuss a regular analytic method of constructing exactly solvable models of quantum mechanics. This method, proposed by Ushveridze (1988c, d) and then generalized by Ushveridze (1989c), is based on the use of one-dimensional exactly solvable equations with several spectral parameters. We will demonstrate that any such equation can be reduced to an exactly solvable Schrôdinger-type equation on a multi-dimensional, in general, curved manifold. The transition to the multi-dimensional case can be realized by means of the inverse method of separation of variables which we discussed briefly in the preceding chapters. Here we will give the most general formulation of this method and describe a convenient procedure of constructing wide classes of exactly solvable multi-parameter spectral equations (mps equations). The corresponding classes of exactly solvable Schrôdinger-type equations will be discussed in the concluding sections of this chapter.
