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Separable quantizations of Stackel systems
Adam Mickiewicz University, Poland.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Polish Academic Science, Poland.
2016 (English)In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 371, 460-477 p.Article in journal (Refereed) Published
Abstract [en]

In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart 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 Stackel system (defined on 2n dimensional Poisson manifold) for which Stackel 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 Stackel system. (C) 2016 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Academic Press, 2016. Vol. 371, 460-477 p.
Keyword [en]
Hamiltonian system; Hamilton-Jacobi equation; Schrodinger equation; Separability; Quantization; Pre-Robertson condition
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-131511DOI: 10.1016/j.aop.2016.06.007ISI: 000381775900023OAI: oai:DiVA.org:liu-131511DiVA: diva2:974417
Note

Funding Agencies|Polish National Science Centre grant [DEC-2011/02/A/ST1/00208]

Available from: 2016-09-26 Created: 2016-09-23 Last updated: 2017-11-21

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The full text will be freely available from 2018-06-14 10:46
Available from 2018-06-14 10:46

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Marciniak, Krzysztof
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  • de-DE
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  • Other locale
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