The stationary method in the abstract theory of scattering

The wave operators and scattering matrix for pairs of self-adjoint operators are constructed in an explicit and invariant form. It is assumed that the perturbation is nuclear or “relatively nuclear”. The equivalence of the stationary and time-dependent versions of the theory is established. The results of the paper may be interpreted as justification for the stationary approach to scattering theory within the framework of the abstract theory of operators.