Levinson's Theorem for Non-local Interactions in Two Dimensions

Details Levinson's Theorem for Non-local Interactions in Two Dimensions Levinson's Theorem for Non-local Interactions in Two Dimensions

1998-06-02

arxiv.org/abs/quant-ph/9806005v1

J.Phys.A31:7501-7510,1998

Physics

Quantum Physics

Latex 11 pages, no figure, submitted to J. Phys. A Email: dongsh@bepc4.ihep.ac.cn, mazq@bepc3.ihep.ac.cn

Scientific paper

10.1088/0305-4470/31/37/010

In the light of the Sturm-Liouville theorem, the Levinson theorem for the Schr\"{o}dinger equation with both local and non-local cylindrically symmetric potentials is studied. It is proved that the two-dimensional Levinson theorem holds for the case with both local and non-local cylindrically symmetric cutoff potentials, which is not necessarily separable. In addition, the problems related to the positive-energy bound states and the physically redundant state are also discussed in this paper.

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