Infinite Quasi-Exactly Solvable Models

Abstract

We introduce a new concept of infinite quasi-exactly solvable models which are constructable through multi-parameter deformations of known exactly solvable ones. The spectral problem for these models admits exact solutions for infinitely many eigenstates but not for the whole spectrum. The hermiticity of their hamiltonians is guaranteed by construction. The proposed models have quasi-exactly solvable classical conterparts.