Spectral properties of a short-range impurity in a quantum dot

DOI10.1063/1.1647693zbMath1068.81021arXivmath-ph/0310040OpenAlexW3106253862MaRDI QIDQ4833358

Jochen Brüning, I. S. Lobanov, Vladimir A. Geyler

Publication date: 15 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0310040

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (7)

On the spectrum of the Schrödinger Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions ⋮ On the spectrum of the Schrödinger Hamiltonian with a particular configuration of three one-dimensional point interactions ⋮ A Quantum Dot with Impurity in the Lobachevsky Plane ⋮ Vladimir A. Geyler ⋮ On the harmonic oscillator on the Lobachevsky plane ⋮ Calculation of the Kirchhoff coefficients for the Helmholtz resonator ⋮ Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

Cites Work

• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• On the ratio of the first two eigenvalues of perturbed harmonic oscillators
• Schrödinger operators with moving point perturbations and related solvable models of quantum mechanical systems
• Potentials of zero radius and Carleman operators
• Schrödinger semigroups
• The theory of extensions and explicitly-soluble models
• Harmonic oscillator Green functions
• Scattering on compact manifolds with infinitely thin horns

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