Isoperiodic classical systems and their quantum counterparts

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dc.creatorAsorey, M.
dc.creatorCarinena, J. F.
dc.creatorMarmo, G.
dc.creatorPerelomov, A.
dc.date2007-07-30
dc.date.accessioned2026-07-07T10:56:57Z
dc.date.available2026-07-07T10:56:57Z
dc.descriptionOne-dimensional isoperiodic classical systems have been first analyzed by Abel. Abel's characterization can be extended for singular potentials and potentials which are not defined on the whole real line. The standard shear equivalence of isoperiodic potentials can also be extended by using reflection and inversion transformations. We provide a full characterization of isoperiodic rational potentials showing that they are connected by translations, reflections or Joukowski transformations. Upon quantization many of these isoperiodic systems fail to exhibit identical quantum energy spectra. This anomaly occurs at order O(h^2) because semiclassical corrections of energy levels of order O(h) are identical for all isoperiodic systems. We analyze families of systems where this quantum anomaly occurs and some special systems where the spectral identity is preserved by quantization. Conversely, we point out the existence of isospectral quantum systems which do not correspond to isoperiodic classical systems.
dc.description29 pages, 8 eps figures
dc.identifierhttps://arxiv.org/abs/0707.4465
dc.identifierhttp://arxiv.org/abs/0707.4465
dc.identifierAnnalsPhys.322:1444-1465,2007
dc.identifierdoi:10.1016/j.aop.2006.07.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186590
dc.subjectHigh Energy Physics - Theory
dc.titleIsoperiodic classical systems and their quantum counterparts
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