(Quasi)-exactly solvable quasinormal modes

TL;DR

This paper explores how to find new potentials with exactly solvable or quasi-exactly solvable quasinormal modes by complexifying parameters in QES models, expanding the class of solvable systems.

Contribution

It introduces a method to generate new QES and exactly solvable quasinormal modes through complexification of parameters in existing QES potentials.

Findings

Identified new potentials with solvable quasinormal modes

Demonstrated complexification as a tool for solvability

Extended QES models based on $sl(2)$ algebra

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.