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Scattering by a bounded non-linear singularity

Published online by Cambridge University Press:  24 October 2008

E. A. Power  and
I. Saavedra
E. A. Power
Affiliation:
Department of Theoretical PhysicsThe UniversityManchester
I. Saavedra
Affiliation:
Department of Theoretical PhysicsThe UniversityManchester
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Abstract

An investigation is made of the effect of a non-linear addition to Schrödinger's equation for s-wave scattering of a beam of particles by a finite region of potential energy. The non-linear region is bounded and of an especially simple form so that an analytic solution is possible. The R-function for the problem is explicitly constructed and some related formulae such as the resonant energies and the scattering length are given. The analytical nature of R as a function of the momentum considered as a complex variable is discussed in relation to causality.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 121 - 130
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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