Quasi Exactly Solvable Difference Equations

Abstract

Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/sin^2x potential deformed by a cos2x potential. They have a finite number of exactly calculable eigenvalues and eigenfunctions.Comment: LaTeX with amsfonts, no figure, 17 pages, a few typos corrected, a reference renewed, 3/2 pages comments on hermiticity adde