Theory of nonbijective canonical transformations in mechanics: Application to the Coulomb problem

DOI10.1063/1.525515zbMath0511.70025OpenAlexW2061547214MaRDI QIDQ4749272

Michel Boiteux

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1063/1.525515

zbMATH Keywords

Hopf fibrationG-structuretotally geodesic submanifoldsisometricCoulomb problemambiguity group of transformationdiastrophic canonical point transformationfibration of Riemannian manifoldsLie group of isometries on fibernonbijective canonical transformationsnonunitary canonical transformations

Mathematics Subject Classification ID

General mathematical topics and methods in quantum theory (81Q99) Global Riemannian geometry, including pinching (53C20) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) Dynamical systems and ergodic theory (37-XX)

Related Items (7)

The Dunkl-Coulomb problem in the plane ⋮ Eigenforms of the spin Laplacian and projectable spinors for principal bundles ⋮ The spectral geometry of the canonical Riemannian submersion of a compact Lie group ⋮ Quantum mechanics on phase space: The hydrogen atom and its Wigner functions ⋮ Generalized canonical transformations for time-dependent systems ⋮ A novel examination of the similarity between a perturbed hydrogen atom and an anharmonic oscillator ⋮ Rydberg states of atoms and molecules. Basic group theoretical and topological analysis

Cites Work

• Canonical transformations to action and angle variables and their representation in quantum mechanics. II. The Coulomb problem
• Canonical transformations to action and angle variables and their representations in quantum mechanics
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• Nonbijective canonical transformations and their representation in quantum mechanics

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