Asymptotic inverse spectral problem for anharmonic oscillators

DOI10.1007/BF01218488zbMath0637.35065WikidataQ61675438 ScholiaQ61675438MaRDI QIDQ1099009

David Gurarie

Publication date: 1987

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

zbMATH Keywords

potentialinverse problemRadon transformperturbationsexplicit solutionreconstructionharmonic oscillatoruniqueasymptotics of spectral shiftsprescribed asymptotics

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Harmonic oscillator perturbed by a decreasing scalar potential, Inverse spectral problem for the 2-sphere Schrödinger operators with zonal potentials, Multiparameter averaging and inverse spectral problem for anharmonic oscillators in \(\mathbb{R}{}^ n\), Asymptotic inverse problem for almost-periodically perturbed quantum harmonic oscillator, Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity, Inverse problem for harmonic oscillator perturbed by potential, characterization

Cites Work

• Eigenvalue distribution theorems for certain homogeneous spaces
• The spectrum of Hill's equation
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• A symbol calculus for a class of pseudodifferential operators on \(S^ n\) and band asymptotics
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Nonclassical eigenvalue asymptotics for operators of Schrödinger type
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