A Class of Matrix Schrödinger Bispectral Operators

2024/01/29 by Brian D. Vasquez Campos, Campos, Brian D. Vasquez
Mathematics · Physics and Astronomy · #35A35 47Fxx 16Dxx #FOS: Mathematics #Numerical methods in inverse problems #Operator Algebras (math.OA) #Optical and Acousto-Optic Technologies #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.16295

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the bispectrality of some class of matrix Schrödinger operators with polynomial potentials that satisfy a second-order matrix autonomous differential equation. The physical equation is constructed using the formal theory of the Laurent series and after that obtaining local solutions using estimations in the Frobenius norm. Furthermore, the characterization of the algebra of polynomial eigenvalues in the spectral variable is given using some family of functions \ P_k\_{k∈ ℕ} with the remarkable property of satisfying a general version of the Leibniz rule.

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