Analytical properties of scattering amplitudes in one-dimensional quantum theory

M. S. Marinov, Bilha Segev

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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.

Original languageEnglish
Pages (from-to)2839-2851
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number11
StatePublished - 1 Dec 1996
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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