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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 137, Number 1, Pages 97–107
DOI: https://doi.org/10.4213/tmf248 (Mi tmf248) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Superintegrable Systems with Third-Order Integrals in Classical and Quantum Mechanics

S. Gravel

Université de Montréal
Full-text PDF (198 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf248
Abstract: We review systems in $E(2)$ that are separable in Cartesian coordinates and admit a third-order integral both in quantum mechanics and in classical mechanics. Differences and similarities between those two cases are illustrated by numerous examples. Many of these superintegrable systems are new, and a relation is seen between superintegrable potentials and Painlevé transcendents.
Keywords: integrals of motion, superintegrability, separation of variables.
English version:
Theoretical and Mathematical Physics, 2003, Volume 137, Issue 1, Pages 1439–1447
DOI: https://doi.org/10.1023/A:1026056823612
Bibliographic databases:
Language: Russian
Citation: S. Gravel, “Superintegrable Systems with Third-Order Integrals in Classical and Quantum Mechanics”, TMF, 137:1 (2003), 97–107; Theoret. and Math. Phys., 137:1 (2003), 1439–1447
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v137/i1/p97
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
     
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