A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials

Abstract

By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new classes of quasi-exactly solvable systems one of which is of periodic type while the other hyperbolic.

LaTeX2e, 8 pages, To appear in J. Phys. A:Mathematical and general(letters)