A Class of Matrix-Valued Schrödinger Operators with Prescribed Finite-Band Spectra

2001/12/12 by Fritz Gesztesy, Gesztesy, Fritz, Lev Sakhnovich +2
Mathematics · Physics and Astronomy · #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.math/0112132

LaTeX, 36 pages

arxiv created 2001/12/12 · openalex publication_date 2001/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a class of matrix-valued Schrödinger operators with prescribed finite-band spectra of maximum spectral multiplicity. The corresponding matrix potentials are shown to be stationary solutions of the KdV hierarchy. The methods employed in this paper rely on matrix-valued Herglotz functions, Weyl--Titchmarsh theory, pencils of matrices, and basic inverse spectral theory for matrix-valued Schrödinger operators.

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