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Letters in Mathematical Physics

, Volume 106, Issue 4, pp 485–507 | Cite as

The Density of Surface States as the Total Time Delay

  • Hermann Schulz-Baldes
Article

Abstract

For a scattering problem of tight-binding Bloch electrons by a weak random surface potential, a generalized Levinson theorem is put forward showing the equality of the total density of surface states and the density of the total time delay. The proof uses explicit formulas for the wave operators in the new rescaled energy and interaction representation, as well as an index theorem for adequate associated operator algebras.

Keywords

surface scattering Levinson theorem 

Mathematics Subject Classification

81U99 47A40 19K56 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany

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