Quantum mechanical resonance and limiting absorption: The many body problem

Abstract

We introduce a notion of quantum mechanical resonance that does not rely on analytic continuation of resolvent or scattering matrix and relate it to slow temporal decay of certain distinguished resonant states. We proceed to prove existence of resonances for the generalized many body Schrodinger operator for a rather large class of potentials containing Coulomb and Yukawa, but also nonsymmetric and nonanalytic potentials with Coulomblike singularities at the origin and certain differentiability and decay properties.