L J Boya et al 1993 J. Phys. A: Math. Gen. 26 5825 doi:10.1088/0305-4470/26/21/020
L J Boya, R F Wehrhahn and A Rivero
Show affiliationsGeometric motion in rank-one symmetric spaces is shown to describe a simple supersymmetric quantum mechanical system. Supersymmetry does indeed lead to a purely algebraic solution for the compact case, providing eigenfunctions and eigenvalues, and also for the Riemannian odd-dimension hyperbolic and Euclidean spaces where SUSY supplies easily the eigenfunctions and hence the phase shifts. In particular, the Jost functions in the latter case are polynomial since the Hamiltonian is seen to be the nth supersymmetric partner of the Hamiltonian of free motion. For the other spaces, supersymmetry proves to be very effective in simplifying and illuminating several aspects of the theory, and suggesting further generalizations.
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
Issue 21 (7 November 1993)
L J Boya et al 1993 J. Phys. A: Math. Gen. 26 5825
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