# Dynamical symmetries for superintegrable quantum systems

## Abstract

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are obtained by generalizing the techniques of factorization of one-dimensional systems. We firstly obtain a pair of noncommuting Lie algebras su(2) that originate the algebra so(4). By considering three spherical coordinate systems, we get the algebra u(3) that can be enlarged by 'reflexions' to so(6). The bounded eigenstates of the Hamiltonian hierarchies are associated to the irreducible unitary representations of these dynamical algebras.

- Authors:

- Universidad de Valladolid, Departmento de Matematica Aplicada (Spain), E-mail: juacal@eis.uva.es
- Universidad de Valladolid, Departmento de Fisica Teorica (Spain), E-mail: olmo@fta.uva.es

- Publication Date:

- OSTI Identifier:
- 21075922

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 3; Other Information: DOI: 10.1134/S1063778807030088; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; EIGENSTATES; FACTORIZATION; HAMILTONIANS; LIE GROUPS; MATHEMATICAL OPERATORS; ONE-DIMENSIONAL CALCULATIONS; REDUCTION; SO-4 GROUPS; SO-6 GROUPS; SPHERICAL CONFIGURATION; SU-2 GROUPS; SYMMETRY; TWO-DIMENSIONAL CALCULATIONS; U-3 GROUPS

### Citation Formats

```
Calzada, J. A., Negro, J., E-mail: jnegro@fta.uva.es, and Olmo, M. A. del.
```*Dynamical symmetries for superintegrable quantum systems*. United States: N. p., 2007.
Web. doi:10.1134/S1063778807030088.

```
Calzada, J. A., Negro, J., E-mail: jnegro@fta.uva.es, & Olmo, M. A. del.
```*Dynamical symmetries for superintegrable quantum systems*. United States. doi:10.1134/S1063778807030088.

```
Calzada, J. A., Negro, J., E-mail: jnegro@fta.uva.es, and Olmo, M. A. del. Thu .
"Dynamical symmetries for superintegrable quantum systems". United States.
doi:10.1134/S1063778807030088.
```

```
@article{osti_21075922,
```

title = {Dynamical symmetries for superintegrable quantum systems},

author = {Calzada, J. A. and Negro, J., E-mail: jnegro@fta.uva.es and Olmo, M. A. del},

abstractNote = {We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are obtained by generalizing the techniques of factorization of one-dimensional systems. We firstly obtain a pair of noncommuting Lie algebras su(2) that originate the algebra so(4). By considering three spherical coordinate systems, we get the algebra u(3) that can be enlarged by 'reflexions' to so(6). The bounded eigenstates of the Hamiltonian hierarchies are associated to the irreducible unitary representations of these dynamical algebras.},

doi = {10.1134/S1063778807030088},

journal = {Physics of Atomic Nuclei},

number = 3,

volume = 70,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}

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