Some remarks on scattering theory in supersymmetric quantum systems

Abstract

First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rⁿ is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.