The perturbatively stable spectrum of a periodic Schrödinger operator

DOI10.1007/BF01231187zbMath0701.34082MaRDI QIDQ914039

Joel Feldmann, Horst Knoerrer, Eugene Trubowitz

Publication date: 1990

Published in: Inventiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

eigenvaluesSchrödinger operatorperturbatively stable spectrum

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (13)

Asymptotic formulae for the Schrödinger operator with Dirichlet and Neumann boundary conditions ⋮ A Semi-Classical K.A.M. Theorem ⋮ Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential ⋮ Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two ⋮ A formula for finding a potential from nodal lines ⋮ Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force ⋮ There is no two dimensional analogue of Lamé's equation ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ On the spectrum of the Schrödinger operator on 𝕋^d: a normal form approach ⋮ An overview of periodic elliptic operators ⋮ Bloch Varieties of Higher-Dimensional, Periodic Schrödinger Operators ⋮ Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori ⋮ On the stable eigenvalues of perturbed anharmonic oscillators in dimension two

Cites Work

• A directional compactification of the complex Bloch variety
• Constructive proof of localization in the Anderson tight binding model
• New approach to the semiclassical limit of quantum mechanics. I: Multiple tunnelings in one dimension
• On isospectral periodic potentials in Rn
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
• Unnamed Item

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