Asymptotic bounds for spectral bands of periodic Schrödinger operators

DOI10.1090/S1061-0022-06-00900-9zbMath1106.35040OpenAlexW1663244194MaRDI QIDQ5481298

Alexander V. Sobolev, Maxim M. Skriganov

Publication date: 9 August 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-06-00900-9

zbMATH Keywords

band spectrumlatticesperiodic operators

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Lattices and convex bodies (number-theoretic aspects) (11H06)

Related Items (7)

Bethe–Sommerfeld Conjecture for Pseudodifferential Perturbation ⋮ On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip ⋮ An overview of periodic elliptic operators ⋮ On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a band with oscillating boundary ⋮ Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip

Cites Work

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• The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
• On the Bethe-Sommerfeld conjecture for the polyharmonic operator.
• Lattice point problems and values of quadratic forms
• Asymptotic of the density of states for the Schrödinger operator with periodic electric potential
• Variation of the number of lattice points in large balls
• Lattice points, perturbation theory and the periodic polyharmonic operator.

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