Band invariants for perturbations of the harmonic oscillator

DOI10.1016/J.JFA.2012.05.022zbMath1248.35134arXiv1109.0567OpenAlexW2009605284MaRDI QIDQ447918

Alejandro Uribe, Victor W. Guillemin, Zuoqin Wang

Publication date: 30 August 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.0567

zbMATH Keywords

inverse spectral problemperturbed harmonic oscillatorband invariants

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Inverse problems for PDEs (35R30) Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (5)

Interface asymptotics of eigenspace Wigner distributions for the harmonic oscillator ⋮ Interfaces in Spectral Asymptotics and Nodal Sets ⋮ On Limiting Eigenvalue Distribution Theorems in Semiclassical Analysis ⋮ The Born approximation in the three-dimensional Calderón problem ⋮ Perturbations of the Landau Hamiltonian: asymptotics of eigenvalue clusters

Cites Work

• Unnamed Item
• Semiclassical spectral invariants for Schrödinger operators
• Inverse spectral problems for Schrödinger operators
• Asymptotics of spectral clusters for a perturbation of the hydrogen atom
• Band invariants and closed trajectories on \(S^ n\)
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Band asymptotics in two dimensions
• Spectral theory on S**2: some open questions
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Clustering for the spectrum of \(h\)-pseudodifferential operators with periodic flow on an energy surface
• Some inverse spectral results for semi-classical Schrödinger operators
• ``Bottom of the well semi-classical trace invariants
• A semiclassical heat trace expansion for the perturbed harmonic oscillator
• An introduction to semiclassical and microlocal analysis
• Fine structure of Zoll spectra

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