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Journal of Mathematical Physics

Schrödinger Scattering Amplitude. III

Alex Grossmann, Tai Tsun Wu

Published Jul 1, 1962• 23 citations
Publisher

Abstract

The methods of an earlier paper are used to obtain a domain of analyticity for the Schrödinger scattering amplitude minus the first Born term. The connection between the scattering integral equation and the Schrödinger equation is also studied.
DOI
10.1063/1.1724270

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One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrödinger equations. The transition and reflection amplitudes are expressed in terms of two complex functions of the incident energy, which are similar to the Jost function in partial-wave scattering. These functions are entire for finite-range potentials and meromorphic for exponentially decreasing potentials. The analytical properties result from the locality of the potential in the wave equation and represent the effect of causality in the time dependence of the scattering process.