### Abstract

We consider a specific differential realization of the su(1,1) algebra and use it to explore such algebraic structures associated with shape-invariant potentials. Our approach combines elements of various methods of solving the Schrodinger equation, such as supersymmetric quantum mechanics (or the factorization method), algebraic techniques and special-function theory. In fact, it amounts to reformulating transformations mapping the Schrodinger equation into the differential equation of orthogonal polynomials in group-theoretical terms. Our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings. The procedure presented here implicitly contains a similar treatment of the compact su(2) algebra as well. Possible generalizations of this approach (involving different realizations of the su(1,1) algebra, other algebraic structures and larger classes of potentials) are also outlined.

Original language | English |
---|---|

Article number | 031 |

Pages (from-to) | 3809-3828 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 27 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Solvable potentials associated with su(1,1) algebras : A systematic study.** / Lévai, G.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 27, no. 11, 031, pp. 3809-3828. https://doi.org/10.1088/0305-4470/27/11/031

}

TY - JOUR

T1 - Solvable potentials associated with su(1,1) algebras

T2 - A systematic study

AU - Lévai, G.

PY - 1994

Y1 - 1994

N2 - We consider a specific differential realization of the su(1,1) algebra and use it to explore such algebraic structures associated with shape-invariant potentials. Our approach combines elements of various methods of solving the Schrodinger equation, such as supersymmetric quantum mechanics (or the factorization method), algebraic techniques and special-function theory. In fact, it amounts to reformulating transformations mapping the Schrodinger equation into the differential equation of orthogonal polynomials in group-theoretical terms. Our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings. The procedure presented here implicitly contains a similar treatment of the compact su(2) algebra as well. Possible generalizations of this approach (involving different realizations of the su(1,1) algebra, other algebraic structures and larger classes of potentials) are also outlined.

AB - We consider a specific differential realization of the su(1,1) algebra and use it to explore such algebraic structures associated with shape-invariant potentials. Our approach combines elements of various methods of solving the Schrodinger equation, such as supersymmetric quantum mechanics (or the factorization method), algebraic techniques and special-function theory. In fact, it amounts to reformulating transformations mapping the Schrodinger equation into the differential equation of orthogonal polynomials in group-theoretical terms. Our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings. The procedure presented here implicitly contains a similar treatment of the compact su(2) algebra as well. Possible generalizations of this approach (involving different realizations of the su(1,1) algebra, other algebraic structures and larger classes of potentials) are also outlined.

UR - http://www.scopus.com/inward/record.url?scp=21344491588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344491588&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/27/11/031

DO - 10.1088/0305-4470/27/11/031

M3 - Article

AN - SCOPUS:21344491588

VL - 27

SP - 3809

EP - 3828

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 11

M1 - 031

ER -