# The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential

## Abstract

The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, corresponds to a quantum superintegrable system, with quadratic and quartic integrals of motion. In this paper we show that the algebra of the integrals is a quadratic ternary algebra, i.e a quadratic extension of a Lie triple system.

- Authors:

- Aristotle University of Thessaloniki, Mathematics Department (Greece)

- Publication Date:

- OSTI Identifier:
- 22043881

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 7; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COULOMB FIELD; INTEGRALS; QUANTUM MECHANICS; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Tanoudis, Y., and Daskaloyannis, C., E-mail: daskalo@math.auth.gr.
```*The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential*. United States: N. p., 2011.
Web. doi:10.1134/S1063778811060299.

```
Tanoudis, Y., & Daskaloyannis, C., E-mail: daskalo@math.auth.gr.
```*The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential*. United States. doi:10.1134/S1063778811060299.

```
Tanoudis, Y., and Daskaloyannis, C., E-mail: daskalo@math.auth.gr. Fri .
"The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential". United States. doi:10.1134/S1063778811060299.
```

```
@article{osti_22043881,
```

title = {The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential},

author = {Tanoudis, Y. and Daskaloyannis, C., E-mail: daskalo@math.auth.gr},

abstractNote = {The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, corresponds to a quantum superintegrable system, with quadratic and quartic integrals of motion. In this paper we show that the algebra of the integrals is a quadratic ternary algebra, i.e a quadratic extension of a Lie triple system.},

doi = {10.1134/S1063778811060299},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 7,

volume = 74,

place = {United States},

year = {2011},

month = {7}

}

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