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Symmetry relations for connection matrices in the phase-integral method

Published online by Cambridge University Press:  24 October 2008

Nanny Fröman ,
Per Olof Fröman  and
Bengt Lundborg
Nanny Fröman
Affiliation:
Institute of Theoretical Physics, University of Uppsala, Thunergsvägen 3, S-752 38 Uppsala, Sweden
Per Olof Fröman
Affiliation:
Institute of Theoretical Physics, University of Uppsala, Thunergsvägen 3, S-752 38 Uppsala, Sweden
Bengt Lundborg
Affiliation:
Institute of Theoretical Physics, University of Uppsala, Thunergsvägen 3, S-752 38 Uppsala, Sweden
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Abstract

In many cases of practical interest there is some kind of symmetry associated with an ordinary second-order differential equation of the Schrödinger type. This symmetry is reflected in certain relations between different F-matrices or different elements of the same F-matrix of the phase-integral method. These symmetry relations imply in turn further relations between the Stokes constants, in addition to those which exist for a general cluster of transition points, and thereby reduce the number of independent Stokes constants. The present paper deals with two important kinds of symmetry relations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 1 , July 1988 , pp. 181 - 191
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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[2]Fröman, N. and Fröman, P. O.. JWKB Approximation, Contributions to the Theory (North-Holland, 1965).Google Scholar
[3]Fröman, N. and Fröman, P. O.. Arbitrary-order phase-integral approximation generated from an unspecified base function. In Méthodes semi-classiques en mécanique quantique (Publications de l'université de Nantes, Institut de Mathématiques et d'informatiques, 1984), pp. 47–53.Google Scholar
[4]Fröman, N., Fröman, P. O. and Lundborg, B.. The Stokes constants for a cluster of transition points. Math. Proc. Cambridge Philos. Soc. 104 (1988), 153–179.CrossRefGoogle Scholar