# Fractional supersymmetry and hierarchy of shape invariant potentials

## Abstract

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians. Special cases of the algebra lead to dynamical systems for which the isospectral supersymmetric partner Hamiltonians are connected by a (translational or cyclic) shape invariance condition.

- Authors:

- Institut de Physique Nucleaire de Lyon, IN2P3-CNRS/Universite Claude Bernard Lyon 1, F-69622 Villeurbanne Cedex (France)

- Publication Date:

- OSTI Identifier:
- 20861554

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2401711; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; HAMILTONIANS; POTENTIALS; QUANTUM MECHANICS; SUPERSYMMETRY

### Citation Formats

```
Daoud, M., and Kibler, M. R.
```*Fractional supersymmetry and hierarchy of shape invariant potentials*. United States: N. p., 2006.
Web. doi:10.1063/1.2401711.

```
Daoud, M., & Kibler, M. R.
```*Fractional supersymmetry and hierarchy of shape invariant potentials*. United States. doi:10.1063/1.2401711.

```
Daoud, M., and Kibler, M. R. Fri .
"Fractional supersymmetry and hierarchy of shape invariant potentials". United States.
doi:10.1063/1.2401711.
```

```
@article{osti_20861554,
```

title = {Fractional supersymmetry and hierarchy of shape invariant potentials},

author = {Daoud, M. and Kibler, M. R.},

abstractNote = {Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians. Special cases of the algebra lead to dynamical systems for which the isospectral supersymmetric partner Hamiltonians are connected by a (translational or cyclic) shape invariance condition.},

doi = {10.1063/1.2401711},

journal = {Journal of Mathematical Physics},

number = 12,

volume = 47,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2401711

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