No abstract

Quantum scattering systems described by Hamiltonians which are constructed from the Casimir operators of certain noncompact groups G are considered. We obtain the following result: If U x and Ux are the Weyl-equivalent representations of the symmetry group G of the dynamical system, the corresponding S matrices are constrained to satisfy SU x ͑g͒ Ux ͑g͒S, for all g [ G. This relation enables one to derive S. As applications, the S matrices corresponding to the dynamical groups SO 0 ͑p, q͒ are derived. [S0031-9007(98)05542-2]

The nonrelativistic quantum scattering problem for a non-central potential which belongs to a class of potentials exhibiting an ‘accidental’ degeneracy is studied. We show that the scattering system under consideration admit the Lie algebra as the potential algebra. The scattering amplitude is then evaluated using purely algebraic techniques to give the closed result. It is expressed in terms of associated Legendre functions.

No abstract

A class of transparent potentials (i.e., potentials with trivial scattering operator S = 1) for the three-dimensional Schrödinger equations is studied. We find the underlying group explaining the transparency phenomenon for these Hamiltonians.