# Exact supersymmetry in the relativistic hydrogen atom in general dimensions--supercharge and the generalized Johnson-Lippmann operator

## Abstract

A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2)) in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.

- Authors:

- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033 (Japan)

- Publication Date:

- OSTI Identifier:
- 20768736

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 3; Other Information: DOI: 10.1063/1.2173173; (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; ATOMS; DEGREES OF FREEDOM; HYDROGEN; POTENTIALS; RELATIVISTIC RANGE; SPIN; SUPERSYMMETRY; VECTORS

### Citation Formats

```
Katsura, Hosho, and Aoki, Hideo.
```*Exact supersymmetry in the relativistic hydrogen atom in general dimensions--supercharge and the generalized Johnson-Lippmann operator*. United States: N. p., 2006.
Web. doi:10.1063/1.2173173.

```
Katsura, Hosho, & Aoki, Hideo.
```*Exact supersymmetry in the relativistic hydrogen atom in general dimensions--supercharge and the generalized Johnson-Lippmann operator*. United States. doi:10.1063/1.2173173.

```
Katsura, Hosho, and Aoki, Hideo. Wed .
"Exact supersymmetry in the relativistic hydrogen atom in general dimensions--supercharge and the generalized Johnson-Lippmann operator". United States.
doi:10.1063/1.2173173.
```

```
@article{osti_20768736,
```

title = {Exact supersymmetry in the relativistic hydrogen atom in general dimensions--supercharge and the generalized Johnson-Lippmann operator},

author = {Katsura, Hosho and Aoki, Hideo},

abstractNote = {A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2)) in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.},

doi = {10.1063/1.2173173},

journal = {Journal of Mathematical Physics},

number = 3,

volume = 47,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2173173

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