### Abstract

Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.

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

Article number | 020 |

Pages (from-to) | 5919-5929 |

Number of pages | 11 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 20 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

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

### Cite this

**Scattering potentials with LS-terms from first-order Casimir operators.** / Lévay, P.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 28, no. 20, 020, pp. 5919-5929. https://doi.org/10.1088/0305-4470/28/20/020

}

TY - JOUR

T1 - Scattering potentials with LS-terms from first-order Casimir operators

AU - Lévay, P.

PY - 1995

Y1 - 1995

N2 - Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.

AB - Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.

UR - http://www.scopus.com/inward/record.url?scp=21844515874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844515874&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/20/020

DO - 10.1088/0305-4470/28/20/020

M3 - Article

AN - SCOPUS:21844515874

VL - 28

SP - 5919

EP - 5929

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 20

M1 - 020

ER -