Space-time picture of semiclassical resonances

This paper addresses the theory of quasiclassical resonances for Schroedinger operators with potentials smooth outside some possible local singularities. We introduce the notion of quasiresonance similar to that of quasimode, but incorporating a condition revealing its scattering nature, and describe its spacetime behaviour. The definition is given in terms of the original Schroedinger operator and uses a description of its frequency set. The result on the space-time behaviour justifies the intuitive picture of resonances as metastable states or 'bound states with finite life-times'. We demonstrate how quasiresonances arise in several natural situations. (orig.)