Prepotential approach to quasinormal modes

TL;DR

This paper introduces a prepotential method to construct and classify models with quasinormal modes, simplifying the process and avoiding the need for symmetry knowledge, while providing explicit potentials, eigenfunctions, and eigenvalues.

Contribution

The paper presents a novel prepotential approach that unifies the construction of exactly and quasi-exactly solvable models with quasinormal modes, bypassing the Lie-algebraic framework.

Findings

Constructed new exactly solvable Morse-like model.

Developed two new quasi-exactly solvable models of Scarf II and P"oschl-Teller types.

Demonstrated the effectiveness of the prepotential approach in classifying models.

Abstract

In this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new models were previously obtained within the Lie-algebraic approach. Unlike the Lie-algebraic approach, the prepotential approach does not require any knowledge of the underlying symmetry of the system. It treats both quasi-exact and exact solvabilities on the same footing, and gives the potential as well as the eigenfunctions and eigenvalues simultaneously. We also present three new models with quasinormal modes: a new exactly solvable Morse-like model, and two new quasi-exactly solvable models of the Scarf II and generalized P\"oschl-Teller types.