### 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 |

### ASJC Scopus subject areas

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