Semiclassical eigenvalues and shape problems on surfaces of revolution

DOI10.1063/1.531095zbMath0826.58041OpenAlexW1968476959WikidataQ125725386 ScholiaQ125725386MaRDI QIDQ4836952

David Gurarie

Publication date: 22 November 1995

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

Full work available at URL: https://semanticscholar.org/paper/109ca0843a3aeed9941ce29389c234e3c1bcb6da

zbMATH Keywords

shapeasymptoticseigenvaluesSchrödinger operatorsmetricsurfaces of revolutionaxisymmetric potentialLaplacians

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (5)

Global transformations preserving Sturm-Liouville spectral data ⋮ Spectral rigidity for spherically symmetric manifolds with boundary ⋮ Symplectic invariants of semitoric systems and the inverse problem for quantum systems ⋮ Semiclassical inverse spectral theory for singularities of focus-focus type ⋮ Inverse spectral theory for semiclassical Jaynes-Cummings systems

Cites Work

• Band invariants and closed trajectories on \(S^ n\)
• Some spectral results for the Laplace operator with potential on the n- sphere
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity
• Can One Hear the Shape of a Drum?

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