Inverse problems, trace formulae for discrete Schrödinger operators

2011/03/11 by Hiroshi Isozaki, Isozaki, Hiroshi, Evgeny Korotyaev +1 · 1 citation
Mathematics · Physics and Astronomy · #35P #81Q #FOS: Mathematics #Numerical methods in inverse problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1103.2193

openalex publication_date 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study discrete Schroedinger operators with compactly supported potentials on the square lattice. 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 for the trace class potentials, and estimate the discrete spectrum in terms of the moments of the spectral shift function and the potential.

Citations

• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Cited by

• Scattering for time periodic Hamiltonians on graphs

Related

• Inverse spectral problem for the Schrödinger operator on the square lattice
• Inverse scattering theory for discrete Schrödinger operators on the hexagonal lattice
• Trace formulae for Schrödinger operators on lattice
• Discretization of inverse scattering on a half line
• An inverse spectral problem for a fractional Schrödinger operator