The Flux-Across-Surfaces Theorem for a Point Interaction Hamiltonian

Details The Flux-Across-Surfaces Theorem for a Point Interaction Hamiltonian The Flux-Across-Surfaces Theorem for a Point Interaction Hamiltonian

1999-08-06

arxiv.org/abs/math-ph/9908008v1

Physics

Mathematical Physics

AMS-Latex file, 11 pages

Scientific paper

The flux-across-surfaces theorem establishes a fundamental relation in quantum scattering theory between the asymptotic outgoing state and a quantity which is directly measured in experiments. We prove it for a hamiltonian with a point interaction, using the explicit expression for the propagator. The proof requires only assuptions on the initial state and it covers also the case of zero-energy resonance. We also outline a different approach based on generalized eigenfunctions, in view of a possible extension of the result.

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