A Lagrangian Fibration of the Isotropic 3-Dimensional Harmonic Oscillator with Monodromy
Autor: | Holger Waalkens, Holger R. Dullin, Konstantinos Efstathiou, Irina Chiscop |
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Přispěvatelé: | Dynamical Systems, Geometry & Mathematical Physics |
Jazyk: | angličtina |
Rok vydání: | 2019 |
Předmět: |
Coordinate system
QUANTUM PHASE-TRANSITIONS HYDROGEN-ATOM 01 natural sciences CLASSIFICATION Hamiltonian system HAMILTONIAN-SYSTEMS NORMALIZATION symbols.namesake 0103 physical sciences 0101 mathematics Mathematics::Symplectic Geometry Mathematical Physics Harmonic oscillator Mathematical physics Physics 010102 general mathematics Fibration Statistical and Nonlinear Physics Prolate spheroidal coordinates RESONANCE Quantum number PERTURBATIONS Monodromy symbols 010307 mathematical physics Hamiltonian (quantum mechanics) |
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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