Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!

dc.creatorNutku, Y.
dc.date2003-06-09
dc.date.accessioned2026-07-07T10:51:06Z
dc.date.available2026-07-07T10:51:06Z
dc.descriptionNambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems.
dc.identifierhttps://arxiv.org/abs/quant-ph/0306059
dc.identifierhttp://arxiv.org/abs/quant-ph/0306059
dc.identifierJ.Phys.A36:7559-7568,2003
dc.identifierdoi:10.1088/0305-4470/36/27/308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184747
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleQuantization with maximally degenerate Poisson brackets: The harmonic oscillator!
dc.typetext

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