On the structure of the essential spectrum for the three-particle Schrödinger operators on lattices

DOI10.1002/MANA.200410509zbMath1121.81046arXivmath-ph/0508029OpenAlexW2078722831MaRDI QIDQ5297186

Zahriddin I. Muminov, Saidachmat Lakaev, Sergio A. Albeverio

Publication date: 18 July 2007

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0508029

zbMATH Keywords

latticeeigenvaluesHamiltoniansessential spectrumdiscrete Schrödinger operatorsshort-range potentialsquasi-momentumFaddeev type equationquantum mechanical two-and three-particle systems

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Applications of operator theory in the physical sciences (47N50) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (14)

On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice ⋮ The essential and discrete spectrum of a model operator associated to a system of three identical quantum particles ⋮ Essential spectrum of a model operator associated with a three-particle system on a lattice ⋮ Infiniteness of the discrete spectrum of two-particle discrete Schrödinger operators ⋮ The essential spectrum of a three particle Schrödinger operator on lattices ⋮ The essential spectrum of the three-particle discrete operator corresponding to a system of three fermions on a lattice ⋮ Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice ⋮ Study of the essential spectrum of a matrix operator ⋮ Existence of bound states of N-body problem in an optical lattice ⋮ On the essential spectrum of three-particle discrete Schrödinger operators with short-range potentials ⋮ Уравнение Фаддеева и местоположение существенного спектра одного трeхчастичного модельного оператора ⋮ О существенном спектре одного модельного оператора, ассоциированного с системой трeх частиц на решeтке ⋮ On the number of eigenvalues of a model operator associated to a system of three-particles on lattices ⋮ Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice

Cites Work

• Unnamed Item
• Scattering theory: some old and new problems
• Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions. I

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