Infinite Quasi-Exactly Solvable Models

TL;DR

This paper introduces a new class of infinite quasi-exactly solvable models constructed via multi-parameter deformations, allowing exact solutions for infinitely many eigenstates while ensuring hermiticity.

Contribution

It presents a novel framework for infinite quasi-exactly solvable models derived from deformations of known exactly solvable systems, with guaranteed hermiticity.

Findings

Models admit exact solutions for infinitely many eigenstates.

Hermiticity of the Hamiltonians is guaranteed by construction.

Models have quasi-exactly solvable classical counterparts.

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.