Scattering and bound state solutions for a class of nonlocal potentials (s-wave) |
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Authors: | M Bertero G Talenti G A Viano |
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Institution: | 1. Institut für Theoretische Kernphysik der Universit?t, Bonn 2. Istituto Matematico dell'Università, Genova 3. Istituto di Fisica dell'Università, Genova
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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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