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Phase-integral treatment of wave reflexion by real potentials

Published online by Cambridge University Press:  24 October 2008

Bengt Lundborg
Bengt Lundborg
Affiliation:
University of Uppsala, Sweden
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Abstract

Approximate analytical expressions for the wave reflexion amplitude for transmission above one-dimensional real smooth and slowly varying potentials in the absence of classical turning points are obtained in two different ways by means of the phase-integral method developed by N. Fröman and P. O. Fröman. The wave reflexion is shown to be governed by the complex transition points for the problem. The great accuracy of the formulae obtained, as well as their respective ranges of applicability, is illustrated by applying them, up to the eleventh order phase-integral approximation, to an exactly solvable model, for which the potential represents a monotonic step.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 493 - 522
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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