# Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

## TL;DR

This paper develops energy-dependent quantum potentials solvable via exceptional orthogonal polynomials, expanding the class of exactly solvable models with explicit solutions in quantum mechanics.

## Contribution

It introduces a method to construct energy-dependent potentials solvable with exceptional orthogonal polynomials using point transformations.

## Key findings

- Several boundary-value problems with discrete spectra
- Explicit normalizable solutions in closed form
- Extension of solvable quantum models

## Abstract

We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.