THE BETHE–SOMMERFELD CONJECTURE FOR THE 3-DIMENSIONAL PERIODIC LANDAU OPERATOR

DOI10.1142/S0129055X04002242zbMath1084.81034WikidataQ123105991 ScholiaQ123105991MaRDI QIDQ5705144

Daniel M. Elton

Publication date: 8 November 2005

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

zbMATH Keywords

Schrödinger operatoruniform magnetic fieldBethe--Sommerfeld conjecture

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (5)

The spectrum of a harmonic oscillator operator perturbed by \(\delta\)-interactions ⋮ Spectra of Schrödinger operators on equilateral quantum graphs ⋮ The spectrum of a harmonic oscillator operator perturbed by point interactions ⋮ An overview of periodic elliptic operators ⋮ Local form-subordination condition and Riesz basisness of root systems

Cites Work

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• A remark on two dimensional periodic potentials
• The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
• On the quantum Hall effect
• On the Bethe-Sommerfeld conjecture for higher-order elliptic operators
• On the density of states for the periodic Schrödinger operator
• Asymptotic of the density of states for the Schrödinger operator with periodic electric potential
• Asymptotic of the density of states for the Schrödinger operator with periodic electromagnetic potential
• Perturbation theory for the Schrödinger operator with a periodic potential
• Lattice points, perturbation theory and the periodic polyharmonic operator.

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