SUPERSYMMETRY AND GEOMETRIC MOTION

Geometric motion in rank-one symmetric spaces is shown to describe a s imple supersymmetric quantum mechanical system. Supersymmetry does ind eed lead to a purely algebraic solution for the compact case, providin g eigenfunctions and eigenvalues, and also for the Riemannian odd-dime nsion hyperbolic and Euclidean spaces where SUSY supplies easily the e igenfunctions and hence the phase shifts. In particular, the Jost func tions 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 s implifying and illuminating several aspects of the theory, and suggest ing further generalizations.