P Lévay 2002 J. Phys. A: Math. Gen. 35 6431 doi:10.1088/0305-4470/35/30/316
P Lévay1,2
Show affiliationsUsing 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.
57N16 Geometric structures on manifolds (See also 57M50)
81Q50 Quantum chaos (See also 37Dxx)
15A90 Applications of matrix theory to physics
81U15 Exactly and quasi-solvable systems
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
Issue 30 (2 August 2002)
Received 28 March 2002
Published 19 July 2002
P Lévay 2002 J. Phys. A: Math. Gen. 35 6431
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