On the spectrum of the two-particle Schrödinger operator with point interaction

DOI10.1134/S1995080221030161zbMath1464.81031OpenAlexW3157305569MaRDI QIDQ2026679

Zahriddin I. Muminov, Utkir Kulzhanov, Shukhrat Lakaev

Publication date: 20 May 2021

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080221030161

zbMATH Keywords

eigenvaluesSchrödinger operatorspoint interactionstwo-body Hamiltonian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Two-body problems (70F05)

Related Items (12)

Invariant subspaces of the Schrödinger operator with a finite support potential ⋮ On the discrete spectra of Schrödinger-type operators on one dimensional lattices ⋮ On the spectrum of two-particle Schrödinger operator with point interaction ⋮ Infiniteness of the discrete spectrum of two-particle discrete Schrödinger operators ⋮ On the number and locations of eigenvalues of the discrete Schrödinger operator on a lattice ⋮ The essential spectrum of a three particle Schrödinger operator on lattices ⋮ On the discrete spectrum of a one-dimensional discrete Schrödinger operator with a perturbation of rank one ⋮ 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 ⋮ The number of eigenvalues of the three-particle Schrödinger operator on three dimensional lattice ⋮ On the spectrum of the one-particle Schrödinger operator with point interaction ⋮ On the number and location of eigenvalues of the two particle Schrödinger operator on a lattice

Cites Work

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• The infinite square well with a point interaction: a discussion on the different parameterizations
• One dimensional models with a singular potential of the type \(-\alpha \delta (x)+\beta \delta^{\prime}(x)\)
• The infinite square well with a singular perturbation
• On the spectrum of the Schrödinger Hamiltonian with a particular configuration of three one-dimensional point interactions
• On pointwise interaction of three distinct particles
• On the spectrum of the Schrödinger Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions
• A remarkable spectral feature of the Schrödinger Hamiltonian of the harmonic oscillator perturbed by an attractive δ′-interaction centred at the origin: double degeneracy and level crossing
• The Hamiltonian of the harmonic oscillator with an attractive $\delta ^{\prime} $-interaction centred at the origin as approximated by the one with a triple of attractive $\delta $-interactions
• On scattering from the one-dimensional multiple Dirac delta potentials
• The discrete spectrum of the spinless one-dimensional Salpeter Hamiltonian perturbed byδ-interactions

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