Asymptotic observables on scattering states (Q796067)

In the framework of quantum mechanical potential scattering theory the asymptotic properties of scattering states for long times are described using selected observables. A quantum mechanical particle moving in n- dimensional space is considered. The state of a particle is described by a vector in the Hilbert space \(L^ 2(R^ n)\). The unitary time evolution is generated by the self adjoint Hamiltonian, which is obtained as a perturbation of the free Hamiltonian. In this paper problems are studied which include a very wide class of potentials which tend in some sense at zero towards infinity. The class of forces include highly singular and very long range potentials. The results may serve as an intermediate step in the proof of asymptotic completeness; as a particular application, a proof of completeness for Coulomb systems is presented.