A Lagrangian Fibration of the Isotropic 3-Dimensional Harmonic Oscillator with MonodromyChiscop, I., Dullin, H. R., Efstathiou, K. & Waalkens, H., Mar-2019, In : Journal of Mathematical Physics. 60, 3, 15 p., 032103.
Research output: Contribution to journal › Article › Academic › peer-review
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.
|Number of pages||15|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - Mar-2019|
- QUANTUM PHASE-TRANSITIONS, HAMILTONIAN-SYSTEMS, HYDROGEN-ATOM, PERTURBATIONS, CLASSIFICATION, NORMALIZATION, RESONANCE
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