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

G. Panati·A. Teta
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Abstract

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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G. Panati, A. Teta. 1999-08-06. The Flux-Across-Surfaces Theorem for a Point Interaction Hamiltonian. https://arxiv.org/abs/math-ph/9908008

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