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Scattering and bound state solutions for a class of nonlocal potentials (s-wave)

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Abstract

Thes-wave scattering solution is discussed for a class of nonlocal (non-separable) potentials. Existence and uniqueness theorems are given and the analyticity domain in thek-variable (k = wave number in the C.M. system) is determined. Furthermore it is proved that solutions of the bound state problem exist and a discussion of the square-integrable solutions, which can occur for a real positive value of the energy, is given. In this last case the scattering solution also exists but it is not unique. Finally theS-matrix is introduced and it is proved that it is unambigously defined even if the scattering solution is not unique.

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Authors and Affiliations

  1. Institut für Theoretische Kernphysik der Universität, Bonn

    M. Bertero

  2. Istituto Matematico dell'Università, Genova

    G. Talenti

  3. Istituto di Fisica dell'Università, Genova

    G. A. Viano

Authors
  1. M. Bertero
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  2. G. Talenti
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  3. G. A. Viano
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Bertero, M., Talenti, G. & Viano, G.A. Scattering and bound state solutions for a class of nonlocal potentials (s-wave). Commun.Math. Phys. 6, 128–150 (1967). https://doi.org/10.1007/BF01654129

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  • DOI: https://doi.org/10.1007/BF01654129

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