The Spectral Shift Function, Friedel Sum Rule, and Levinson Theorem

Details The Spectral Shift Function, Friedel Sum Rule, and Levinson Theorem The Spectral Shift Function, Friedel Sum Rule, and Levinson Theorem

2011-11-25

arxiv.org/abs/1111.5939v1

Physics

Mathematical Physics

76 pages, no figure

Scientific paper

We examine three trace formulas, the spectral shift function, Friedel sum rule and Levinson theorem in potential scattering theory. Although these formulas are closely related to each other, they have been often formulated in different settings so far. We propose a unified treatment for them. First we construct the spectral shift function in an alternative way, and then we prove that the spectral shift function thus constructed yields Friedel sum rule and Levinson theorem in arbitrary dimensions without assuming spherical symmetry of the potential.

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