Perturbatively unstable eigenvalues of a periodic Schrödinger operator

DOI10.1007/BF02566665zbMath0763.35024OpenAlexW2017573532MaRDI QIDQ1190208

Eugene Trubowitz, Joel Feldman, Horst Knoerrer

Publication date: 27 September 1992

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02566665

zbMATH Keywords

Floquet spectrumcrystal momentumapproximation of eigenfunctions by quasimodesstability of Floquet eigenvalues

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Schrödinger operator, Schrödinger equation (35J10)

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KAM for PDEs ⋮ Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one ⋮ Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential ⋮ Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential ⋮ Quasi-periodic solutions of nonlinear Schrödinger equations on \(T^{d}\) ⋮ Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two ⋮ Asymptotic formulae for the Bloch eigenvalues near planes of diffraction ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ An overview of periodic elliptic operators ⋮ Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori ⋮ On the stable eigenvalues of perturbed anharmonic oscillators in dimension two

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