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

## Abstract

We construct energy-dependent potentials for which the Schrödinger equations admit solutions 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.

- Authors:

- Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States)
- (United States)
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

- Publication Date:

- OSTI Identifier:
- 22617483

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY-VALUE PROBLEMS; LAGUERRE POLYNOMIALS; MATHEMATICAL SOLUTIONS; SCHROEDINGER EQUATION

### Citation Formats

```
Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408, and Roy, Pinaki, E-mail: pinaki@isical.ac.in.
```*Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.01.023.

```
Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408, & Roy, Pinaki, E-mail: pinaki@isical.ac.in.
```*Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials*. United States. doi:10.1016/J.AOP.2017.01.023.

```
Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408, and Roy, Pinaki, E-mail: pinaki@isical.ac.in. Wed .
"Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials". United States.
doi:10.1016/J.AOP.2017.01.023.
```

```
@article{osti_22617483,
```

title = {Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials},

author = {Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408 and Roy, Pinaki, E-mail: pinaki@isical.ac.in},

abstractNote = {We construct energy-dependent potentials for which the Schrödinger equations admit solutions 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.},

doi = {10.1016/J.AOP.2017.01.023},

journal = {Annals of Physics},

number = ,

volume = 378,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}

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