On eigenvalues in gaps for perturbed magnetic Schrödinger operators

DOI10.1063/1.532308zbMath0916.47054OpenAlexW2035182765MaRDI QIDQ4212618

Serge Z. Levendovskij, Rainer Hempel

Publication date: 6 July 1999

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

Full work available at URL: https://semanticscholar.org/paper/f652ab11d58ff6da4ee17cb9c4140ffb16ec7d99

zbMATH Keywords

eigenvaluesSchrödinger operatormagnetic fieldelectric potentialspectral gapperturbed operatorelectric and magnetic perturbation

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theory of linear operators (47A55) Electromagnetic interaction; quantum electrodynamics (81V10) 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

Eigenvalue Asymptotics for Weakly Perturbed Dirac and Schrödinger Operators with Constant Magnetic Fields of Full Rank, Eigenvalues in spectral gaps of the two-dimensional Pauli operator, A trace formula and high-energy spectral asymptotics for the perturbed Landau Hamiltonian, Low energy asymptotics of the spectral shift function for Pauli operators with nonconstant magnetic fields, Strong-electric-field eigenvalue asymptotics for the Iwatsuka model, The extraordinary spectral properties of radially periodic Schrödinger operators

Cites Work

• The discrete spectrum in the gaps of a second-order perturbed periodic operator
• Effet d'Aharonov-Bohm sur un état borné de l'équation de Schrödinger. (Aharonov-Bohm effect for a bounded state of the Schrödinger equation)
• On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• Trapping and cascading of eigenvalues in the large coupling limit
• Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• Eigenvalues in gaps and decoupling by Neumann boundary conditions
• Schrödinger operators with magnetic fields. I: General interactions
• Strong-electric-field eigenvalue asymptotics for the perturbed magnetic Schrödinger operator
• The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator \(H-\lambda W\) in a gap of \(H\)
• Strong magnetic fields, Dirichlet boundaries, and spectral gaps