Resonances of quantum mechanical scattering systems and Lax-Phillips scattering theory

For selected classes of quantum mechanical scattering systems a canonical association of a decay semigroup is presented. The spectrum of the generator of this semigroup is a pure eigenvalue spectrum and it coincides with the set of all resonances. The essential condition for the results is the meromorphic continuability of the scattering matrix onto C \ (-infinity, 0] and the rims R_ +/- i0. Further finite multiplicity is assumed. The approach is based on an adaption of the Lax-Phillips scattering theory to semibounded Hamiltonians. It is applied to trace class perturbations with analyticity conditions. A further example is the potential scattering for central-symmetric potentials with compact support and angular momentum 0. (c) 2010, American Institute of Physics. [doi:10.1063/1.3504174]