# Potentials of the Heun class: The triconfluent case

## Abstract

We study special classes of potentials for which the one-dimensional (or radial) Schrödinger equation can be reduced to a triconfluent Heun equation by a suitable coordinate transformation together with an additional transformation of the wave function. In particular, we analyze the behaviour of those subclasses of the potential arising when the ordinary differential equation governing the coordinate transformation admits explicit analytic solutions in terms of the radial variable. Furthermore, we obtain formulae for solutions of the eigenvalue problem of the associated radial Schrödinger operator. Last but not least, using methods of supersymmetric quantum mechanics we relate the considered potentials to a new class of exactly solvable ones.

- Authors:

- Department of Mathematics, University of the West Indies, Kingston 6 (Jamaica)
- Departamento de Fisica, Universidad de los Andes, Cra. 1E No. 18A-10, Bogota (Colombia)

- Publication Date:

- OSTI Identifier:
- 22403142

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; DIFFERENTIAL EQUATIONS; EIGENVALUES; EXACT SOLUTIONS; QUANTUM MECHANICS; SUPERSYMMETRY; WAVE FUNCTIONS

### Citation Formats

```
Batic, D., E-mail: davide.batic@uwimona.edu.jm, Mills-Howell, D., E-mail: dominic.millz27@gmail.com, and Nowakowski, M., E-mail: mnowakos@uniandes.edu.co.
```*Potentials of the Heun class: The triconfluent case*. United States: N. p., 2015.
Web. doi:10.1063/1.4921344.

```
Batic, D., E-mail: davide.batic@uwimona.edu.jm, Mills-Howell, D., E-mail: dominic.millz27@gmail.com, & Nowakowski, M., E-mail: mnowakos@uniandes.edu.co.
```*Potentials of the Heun class: The triconfluent case*. United States. doi:10.1063/1.4921344.

```
Batic, D., E-mail: davide.batic@uwimona.edu.jm, Mills-Howell, D., E-mail: dominic.millz27@gmail.com, and Nowakowski, M., E-mail: mnowakos@uniandes.edu.co. Fri .
"Potentials of the Heun class: The triconfluent case". United States. doi:10.1063/1.4921344.
```

```
@article{osti_22403142,
```

title = {Potentials of the Heun class: The triconfluent case},

author = {Batic, D., E-mail: davide.batic@uwimona.edu.jm and Mills-Howell, D., E-mail: dominic.millz27@gmail.com and Nowakowski, M., E-mail: mnowakos@uniandes.edu.co},

abstractNote = {We study special classes of potentials for which the one-dimensional (or radial) Schrödinger equation can be reduced to a triconfluent Heun equation by a suitable coordinate transformation together with an additional transformation of the wave function. In particular, we analyze the behaviour of those subclasses of the potential arising when the ordinary differential equation governing the coordinate transformation admits explicit analytic solutions in terms of the radial variable. Furthermore, we obtain formulae for solutions of the eigenvalue problem of the associated radial Schrödinger operator. Last but not least, using methods of supersymmetric quantum mechanics we relate the considered potentials to a new class of exactly solvable ones.},

doi = {10.1063/1.4921344},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 56,

place = {United States},

year = {2015},

month = {5}

}