On the discrete spectrum of two-particle discrete Schrödinger operators

2011/03/16 by Zahriddin Muminov, Muminov, Z. I.
Mathematics · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1103.3132

openalex publication_date 2011/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper our aim is to explore some spectral properties of the family two-particle discrete Schrödinger operators h^d(k)=h^d₀(k)+ v, k∈ \T^d, on the d dimensional lattice \Z^d, d≥ 1, k being the two-particle quasi-momentum. Under some condition in the case k∈ \T^d∖ (-π,π)^d, we establish necessary and sufficient conditions for existence of infinite discrete spectrum of the operator h^d(k).

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