Separable quantizations of Stäckel systems
| Autor: | Maciej Blaszak, Krzysztof Marciniak, Ziemowit Domański |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics
Quantum Physics Hamiltonian system Hamilton-Jacobi equation Schrodinger equation Separability Quantization Pre-Robertson condition Pure mathematics Monomial Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics Geometry General Physics and Astronomy Riemannian geometry 01 natural sciences Hamilton–Jacobi equation Schrödinger equation Separable space symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Quadratic equation 37K10 70H06 70H20 53D55 81S10 Poisson manifold 0103 physical sciences symbols Geometri 0101 mathematics 010306 general physics |
| Zdroj: | Annals of Physics. 371:460-477 |
| ISSN: | 0003-4916 |
| DOI: | 10.1016/j.aop.2016.06.007 |
| Popis: | In this article we prove that many Hamiltonian systems that can not be separably quantized in the classical approach of Robertson and Eisenhardt can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta St\"ackel system (defined on a 2n-dimensional Poisson manifold) for which the St\"ackel matrix consists of monomials in position coordinates there exist infinitely many quantizations - parametrized by n arbitrary functions - that turn this system into a quantum separable St\"ackel system. Comment: We added the journal reference and also intorduced several minor amendmends |
| Databáze: | OpenAIRE |
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