On the trace-class method in potential scattering theory

One considers a perturbation of Schrödinger operator $H_0$ with an arbitrary bounded potential by a function $q$ which is vanishing sufficiently quickly at infinity. Trace-class theorems are applied to prove existence and completeness of wave operators for corresponding Hamiltonians $H_0$, $H=H_0+q$. Generalizations to broader class of unperturbed operators as well as to perturbations by first-order differential operators are given. Moreover, perturbations by integral operators of Fourier type are considered.