Propagation properties of quantum scattering states (Q796068)

This paper considers the motion of a quantum mechanical particle of mass m moving in n-dimensional space which is influenced by a potential. The initial state is supposed to be localized inside a ball of radius R and with energy bounded above by \(mv^ 2/2\). With these assumptions one has that the component of a state in the classically forbidden region \(| x|>R+v| t|\) vanishes asymptotically in time. Various estimates are presented for the free time evolution. The momentum support of a state in terms of its full energy support in regions, where the potential is weak, is controlled.