Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)