Siegert pseudostate formulation of scattering theory: General three-dimensional case

Lev O. Krainov, Pavel A. Batishchev, and Oleg I. Tolstikhin
Phys. Rev. A 93, 042706 – Published 20 April 2016

Abstract

This paper generalizes the Siegert pseudostate (SPS) formulation of scattering theory to arbitrary finite-range potentials without any symmetry in the three-dimensional (3D) case. The orthogonality and completeness properties of 3D SPSs are established. The SPS expansions for scattering states, outgoing-wave Green's function, scattering matrix, and scattering amplitude, that is, all major objects of scattering theory, are derived. The theory is illustrated by calculations for several model potentials. The results enable one to apply 3D SPSs as a purely discrete basis capable of representing both discrete and continuous spectra in solving various stationary and time-dependent quantum-mechanical problems.

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  • Received 22 March 2016

DOI:https://doi.org/10.1103/PhysRevA.93.042706

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Lev O. Krainov1, Pavel A. Batishchev2, and Oleg I. Tolstikhin1

  • 1Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
  • 2NewStore GmbH, Schiffbauerdamm 22, 10117 Berlin, Germany

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Issue

Vol. 93, Iss. 4 — April 2016

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