Quantized Neumann problem, separable potentials on S n and the Lamè equation

DOI10.1063/1.531347zbMath0843.35067OpenAlexW1974399101MaRDI QIDQ4873439

David Gurarie

Publication date: 13 May 1996

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

Full work available at URL: https://doi.org/10.1063/1.531347

zbMATH Keywords

separable potentialsseparation of variablescommuting integralsinverse spectral problem on the spherequantum Neumann-Hamiltonian

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Inverse scattering problems in quantum theory (81U40) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (6)

ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ) ⋮ The Gauss-Knörrer map for the Rosochatius dynamical system ⋮ Spectrum of the quantum Neumann model ⋮ The quantum Neumann model: asymptotic analysis ⋮ Simultaneous separation for the Neumann and Chaplygin systems ⋮ The quantum Neumann model: refined semiclassical results

Cites Work

• Verdier elliptic solitons and the Weierstrass theory of reduction
• Band invariants and closed trajectories on \(S^ n\)
• Some spectral results for the Laplace operator with potential on the n- sphere
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity
• The Lamé wave equation
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES

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