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Russian Physics Journal

The generalized WKB method in the three-dimensional case. II

Н. И. Жирнов, F. B. Nurlygayanov

Published Mar 1, 1976• 0 citations
Publisher
DOI
10.1007/bf00945694

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For pt.I see ibid., vol.20, p.397-409, 1987. The spectrum of an ellipsoidal box of prolate and oblate symmetry are calculated by an extract diagonalisation and by semiclassical methods. The influence of a separatrix in phase space is analysed with the help of the WKB phases derived in an earlier paper. Differences between the prolate the oblate L z =0 states are explained using this separatrix. It is found that the EBK method, improved by the uniform approximation, leads to a spectrum in very good agreement with the wave mechanical results. The spectrum of a two-dimensional elliptical membrane ('billiard' box) is also studied with similar conclusions.

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For pt.I see ibid., vol.20, p.397-409, 1987. The spectrum of an ellipsoidal box of prolate and oblate symmetry are calculated by an extract diagonalisation and by semiclassical methods. The influence of a separatrix in phase space is analysed with the help of the WKB phases derived in an earlier paper. Differences between the prolate the oblate L z =0 states are explained using this separatrix. It is found that the EBK method, improved by the uniform approximation, leads to a spectrum in very good agreement with the wave mechanical results. The spectrum of a two-dimensional elliptical membrane ('billiard' box) is also studied with similar conclusions.