Inverse Problems, Trace Formulae for Discrete Schrödinger Operators

By Hiroshi Isozaki, E. Korotyaev. 2011

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We study discrete Schrödinger operators with compactly supported potentials on Zd. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely reconstructed from the S-matrix of all energies. We also study the spectral shift function $${\xi(\lambda)}$$ for the trace class potentials, and estimate the discrete spectrum in terms of the moments of $${\xi(\lambda)}$$ and the potential.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3c6aba481cb800bfc39f4a129ec8be6437b40538