97-562 Guerin C.A

One-dimensional quantum scattering for potentials defined as measures (71K, DVI file) Nov 2, 97

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Abstract. We generalize the basic one-dimensional scattering formalism to potentials defined as measures and retrieve the classical results that hold for smooth potentials. We introduce a set of generalized eigenfunctions for the corresponding Schr{\" o}dinger operator and study their analytical properties. This allows a characterization of the spectrum and an eigenfunction expansion. We also prove the existence and completeness of the wave operators and give explicit formulae for these latter.

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