The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

DOI10.1007/s11232-009-0030-6zbMath1175.81100OpenAlexW2141603525MaRDI QIDQ1034434

I. N. Bozorov, Saidachmat Lakaev

Publication date: 6 November 2009

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-009-0030-6

zbMATH Keywords

eigenvaluecontinuous spectrumBirman-Schwinger operatorFredholm determinantvirtual levelone-particle Hamiltonian

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (20)

On the number of eigenvalues of the lattice model operator in one-dimensional case ⋮ Threshold of discrete Schrödinger operators with delta potentials on n-dimensional lattice ⋮ Unnamed Item ⋮ The number and location of eigenvalues for the two-particle Schrödinger operators on lattices ⋮ On the number and locations of eigenvalues of the discrete Schrödinger operator on a lattice ⋮ On the discrete spectrum of a one-dimensional discrete Schrödinger operator with a perturbation of rank one ⋮ Threshold effects in a two-fermion system on an optical lattice ⋮ On the existence of bound states of a system of two fermions on the two-dimensional cubic lattice ⋮ Puiseux series expansion for eigenvalue of the generalized Friedrichs model with the perturbation of rank one ⋮ Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions ⋮ Threshold analysis of the three dimensional lattice Schrödinger operator with non-local potential ⋮ The existence and asymptotics of eigenvalues of Schrödinger operator on two dimensional lattices ⋮ On the number and location of eigenvalues of the two particle Schrödinger operator on a lattice ⋮ Spectral properties of a two-particle Hamiltonian on a lattice ⋮ Spectral and threshold analysis of a small rank perturbation of the discrete Laplacian ⋮ The exact number of eigenvalues of the discrete Schrödinger operators in one-dimensional case ⋮ On compact perturbation of two-particle Schrödinger operator on a lattice ⋮ Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice ⋮ Spectral properties of the discrete Schrödinger operator with non-local potential ⋮ Bose–Hubbard models with on-site and nearest-neighbor interactions: exactly solvable case

Cites Work

• Unnamed Item
• The threshold effects for the two-particle Hamiltonians on lattices
• The symmetry and Efimov's effect in systems of three-quantum particles
• Large time behavior of the \(L^ p\) norm of Schrödinger semigroups
• On Efimov's effect in a system of three identical quantum particles
• Merging of eigenvalues and resonances of a two-particle Schrödinger operator
• On the spectrum of an Hamiltonian in Fock space. Discrete spectrum asymptotics
• The spectrum of two-particle bound states of transfer matrices of Gibbs fields (fields on a two-dimensional lattice: adjacent levels).
• ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR

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