Spectrum of the two-particle Schrödinger operator on a lattice View Full Text


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Article Info

DATE

2008-05

AUTHORS

S. N. Lakaev, A. M. Khalkhuzhaev

ABSTRACT

We consider the family of two-particle discrete Schrödinger operators H(k) associated with the Hamiltonian of a system of two fermions on a ν-dimensional lattice ℤ, ν ≥, 1, where k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{T}^\nu $$ \end{document} ≡ (− π, π]ν is a two-particle quasimomentum. We prove that the operator H(k), k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{T}^\nu $$ \end{document}, k ≠ 0, has an eigenvalue to the left of the essential spectrum for any dimension ν = 1, 2, ... if the operator H(0) has a virtual level (ν = 1, 2) or an eigenvalue (ν ≥ 3) at the bottom of the essential spectrum (of the two-particle continuum). More... »

PAGES

754

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11232-008-0064-1

DOI

http://dx.doi.org/10.1007/s11232-008-0064-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009581998


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