Fundamentals of scattering theory and resonances in quantum mechanics

abstract we present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. the wave operators and s-matrix are constructed for smooth, compactly-supported potential perturbations of the laplacian. the meromorphic continuation of the cut-off resolvent is proved for the same family of schr？dinger operators. quantum resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent. these are shown to be the same as the poles of the meromorphically continued s-matrix. the basic problems of the existence of resonances and estimates on the resonance counting function are described and recent results are presented.