Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator

DOI10.1007/s11232-012-0076-8zbMath1282.81079OpenAlexW2015925691MaRDI QIDQ2636638

Shukhrat Lakaev, A. M. Khalkhuzhaev, Saidachmat Lakaev

Publication date: 30 January 2014

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

Full work available at URL: https://doi.org/10.1007/s11232-012-0076-8

zbMATH Keywords

eigenvalueasymptotic expansionHamiltonianessential spectrumFredholm determinantdiscrete Schrödinger operatoreigenvalue expansionquasimomentum

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Discrete version of topics in analysis (39A12)

Related Items (15)

Expansion of eigenvalues of the perturbed discrete bilaplacian ⋮ On the spectrum of Schrödinger-type operators on two dimensional lattices ⋮ Bound states of the Schrödinger operator of a system of three bosons on a lattice ⋮ On the discrete spectra of Schrödinger-type operators on one dimensional lattices ⋮ The spectrum of a non-local discrete Schrödinger operator with a delta potential on the one-dimentional lattice ⋮ 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 ⋮ Puiseux series expansion for eigenvalue of the generalized Friedrichs model with the perturbation of rank one ⋮ 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 ⋮ Bound states of Schrödinger-type operators on one and two dimensional lattices ⋮ On spectrum of the discrete bilaplacian with zero-range perturbation ⋮ Convergent expansions of eigenvalues of the generalized Friedrichs model with a rank-one perturbation ⋮ Threshold analysis of the one-rank perturbation non-local discrete Laplacian ⋮ 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
• On the bound state of Schrödinger operators in one dimension
• Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Asymptotics of eigenvalues of two-particle Schrödinger operators on lattices with zero range interaction

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