Quasi-exactly solvable quasinormal modes

TL;DR

This paper explores how quasi-exactly solvable models can be extended to include quasinormal modes with complex energies by complexifying parameters, leading to new exactly solvable potentials.

Contribution

It introduces a method to generate new QES and exactly solvable potentials with quasinormal modes through parameter complexification of existing QES models.

Findings

Found new potentials with QES quasinormal modes

Derived one QES and four exactly solvable potentials

Extended the class of solvable models with complex energies

Abstract

We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes by suitable complexification of parameters defining the QES potentials. Particularly, we obtain one QES and four exactly solvable potentials out of the five one-dimensional QES systems based on the $sl(2)$ algebra.