On the multiplicities of the spectrum for quasi-classical mechanics on spheres

DOI10.2748/tmj/1178229911zbMath0406.58027OpenAlexW1995538544MaRDI QIDQ1257730

Il Kiyotaka

Publication date: 1978

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229911

zbMATH Keywords

Geodesic FlowEigenvalue of the Laplace-Beltrami OperatorLagrangian FoliationMaslov's Quantization ConditionQuasi-Classical Mechanics on Spheres

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Foliations in differential topology; geometric theory (57R30) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (4)

The quantization condition in the presence of a magnetic field and quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field ⋮ Geometric quantization for the mechanics on spheres ⋮ Bloch theory and quantization of magnetic systems ⋮ Geometric quantization of the multidimensional Kepler problem

Cites Work

• A construction of fundamental solution of Schrödinger's equation on the spheres
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
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