### Abstract

Using the theory of induced representations two exactly solvable models of non-relativistic scattering with SL(2, C) symmetry are presented. The first describes the scattering of a charged particle moving on the Poincaré upper half space H under the influence of an SU(2) non-Abelian gauge potential with isospin s. The second deals with a one-dimensional coupled-channel scattering problem for a charged particle in a matrix-valued scalar potential containing Morse-like interaction terms. The coupled channel wavefunctions and the corresponding scattering matrices are calculated. A detailed description of the underlying geometric structures is also given and a generalization for restricting the motion to fundamental domains of H (three manifolds of constant negative sectional curvature) is outlined. Such models provide an interesting generalization to the known ones of multichannel scattering, quantum chaos and chaotic cosmology.

Original language | English |
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Pages (from-to) | 6431-6457 |

Number of pages | 27 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 30 |

DOIs | |

Publication status | Published - Aug 2 2002 |

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### ASJC Scopus subject areas

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

### Cite this

**Exactly solvable models of scattering with SL(2, C) symmetry.** / Lévay, P.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 35, no. 30, pp. 6431-6457. https://doi.org/10.1088/0305-4470/35/30/316

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TY - JOUR

T1 - Exactly solvable models of scattering with SL(2, C) symmetry

AU - Lévay, P.

PY - 2002/8/2

Y1 - 2002/8/2

N2 - Using the theory of induced representations two exactly solvable models of non-relativistic scattering with SL(2, C) symmetry are presented. The first describes the scattering of a charged particle moving on the Poincaré upper half space H under the influence of an SU(2) non-Abelian gauge potential with isospin s. The second deals with a one-dimensional coupled-channel scattering problem for a charged particle in a matrix-valued scalar potential containing Morse-like interaction terms. The coupled channel wavefunctions and the corresponding scattering matrices are calculated. A detailed description of the underlying geometric structures is also given and a generalization for restricting the motion to fundamental domains of H (three manifolds of constant negative sectional curvature) is outlined. Such models provide an interesting generalization to the known ones of multichannel scattering, quantum chaos and chaotic cosmology.

AB - Using the theory of induced representations two exactly solvable models of non-relativistic scattering with SL(2, C) symmetry are presented. The first describes the scattering of a charged particle moving on the Poincaré upper half space H under the influence of an SU(2) non-Abelian gauge potential with isospin s. The second deals with a one-dimensional coupled-channel scattering problem for a charged particle in a matrix-valued scalar potential containing Morse-like interaction terms. The coupled channel wavefunctions and the corresponding scattering matrices are calculated. A detailed description of the underlying geometric structures is also given and a generalization for restricting the motion to fundamental domains of H (three manifolds of constant negative sectional curvature) is outlined. Such models provide an interesting generalization to the known ones of multichannel scattering, quantum chaos and chaotic cosmology.

UR - http://www.scopus.com/inward/record.url?scp=0041380841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041380841&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/30/316

DO - 10.1088/0305-4470/35/30/316

M3 - Article

VL - 35

SP - 6431

EP - 6457

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 30

ER -