# Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

## Abstract

Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.

- Authors:

- Department of Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov Str., Lviv, UA-79005 (Ukraine)

- Publication Date:

- OSTI Identifier:
- 22403079

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COMMUTATION RELATIONS; DE SITTER GROUP; DE SITTER SPACE; ENERGY SPECTRA; OSCILLATORS; QUANTUM MECHANICS; SUPERSYMMETRY

### Citation Formats

```
Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua.
```*Dirac oscillator and nonrelativistic Snyder-de Sitter algebra*. United States: N. p., 2015.
Web. doi:10.1063/1.4905085.

```
Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua.
```*Dirac oscillator and nonrelativistic Snyder-de Sitter algebra*. United States. doi:10.1063/1.4905085.

```
Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua. Thu .
"Dirac oscillator and nonrelativistic Snyder-de Sitter algebra". United States.
doi:10.1063/1.4905085.
```

```
@article{osti_22403079,
```

title = {Dirac oscillator and nonrelativistic Snyder-de Sitter algebra},

author = {Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua},

abstractNote = {Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.},

doi = {10.1063/1.4905085},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 56,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}

DOI: 10.1063/1.4905085

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