Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!
| dc.creator | Nutku, Y. | |
| dc.date | 2003-06-09 | |
| dc.date.accessioned | 2026-07-07T10:51:06Z | |
| dc.date.available | 2026-07-07T10:51:06Z | |
| dc.description | Nambu'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.identifier | https://arxiv.org/abs/quant-ph/0306059 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0306059 | |
| dc.identifier | J.Phys.A36:7559-7568,2003 | |
| dc.identifier | doi:10.1088/0305-4470/36/27/308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/184747 | |
| dc.subject | Quantum Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Quantization with maximally degenerate Poisson brackets: The harmonic oscillator! | |
| dc.type | text |