On quasi-exactly solvable matrix models

TL;DR

This paper introduces a new method for constructing quasi-exactly solvable matrix models using the properties of sl(2,R) algebra representations and their invariant subspaces within matrix differential operators.

Contribution

It proposes an efficient procedure leveraging sl(2,R) algebra representations to develop quasi-exactly solvable matrix models, expanding the toolkit for solving complex quantum systems.

Findings

The method identifies finite dimensional invariant subspaces in matrix differential operators.

It demonstrates the construction of new quasi-exactly solvable matrix models.

The approach simplifies the process of finding solvable models in quantum mechanics.

Abstract

An efficient procedure for constructing quasi-exactly solvable matrix models is suggested. It is based on the fact that the representation spaces of representations of the algebra sl(2,R) within the class of first-order matrix differential operators contain finite dimensional invariant subspaces.