POINCARE RESONANCES AND THE LIMITS OF QUANTUM-MECHANICS

In previous papers we have shown that the elimination of the resonance divergences in large Poincare systems leads to complex irreducible sp ectral representations of the Liouville-von Neumann operator. This lea ds to an extended formulation of quantum theory on the level of densit y matrices. We consider in this paper potential scattering. Our theory applies to persistent scattering (beyond the S-matrix approach). Nume rical simulations show quantitative agreement with our predictions.