A Lagrangian Fibration of the Isotropic 3-Dimensional Harmonic Oscillator with Monodromy

Autor: Holger Waalkens, Holger R. Dullin, Konstantinos Efstathiou, Irina Chiscop
Přispěvatelé: Dynamical Systems, Geometry & Mathematical Physics
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Journal of Mathematical Physics, 60(3):032103. AMER INST PHYSICS
ISSN: 0022-2488
DOI: 10.1063/1.5053887
Popis: The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three Poisson commuting integrals and, correspondingly, three commuting operators, one of which is the Hamiltonian. We show that the Lagrangian fibration defined by the Hamiltonian, the z component of the angular momentum, and a quartic integral obtained from separation in prolate spheroidal coordinates has a non-degenerate focus-focus point, and hence, non-trivial Hamiltonian monodromy for sufficiently large energies. The joint spectrum defined by the corresponding commuting quantum operators has non-trivial quantum monodromy implying that one cannot globally assign quantum numbers to the joint spectrum. Published under license by AIP Publishing.
Databáze: OpenAIRE
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