@article{2019_CDEW_Oscillator_Monodromy,
abstract = {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.},
archiveprefix = {arxiv},
author = {Chiscop, I. and Dullin, H. R. and Efstathiou, K. and Waalkens, H.},
doi = {10.1063/1.5053887},
eprint = {1808.08908},
journal = {Journal of Mathematical Physics},
journalurl = {https://aip.scitation.org/journal/jmp},
number = {3},
pages = {032103},
primaryclass = {math-ph},
title = {A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy},
volume = {60},
year = {2019}
}