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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 93, Number 1, Pages 3–16 (Mi tmf5725)  
This article is cited in 5 scientific papers (total in 5 papers)

Jacobi algebra and potentials generated by it

I. M. Lutsenko

Donetsk State University
Full-text PDF (1316 kB) Citations (5)
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Abstract: It is shown that the Jacobi algebra QJ(3)QJ(3) generates potentials that admit exact solution in relativistic and nonrelativistic quantum mechanics. Being a spectrum-generatingdynamic symmetry algebra and possessing the ladder property, QJ(3)QJ(3) makes it possible to find the wave functions in the coordinate representation. The exactly solvable potentials specified in explicit form are regarded as a special case of a larger class of exactly solvable potentials specified implicitly. The connection between classical and quantum problems possessing exact solutions is obtained by means of QJ(3)QJ(3).
Received: 23.09.1991
Revised: 26.04.1992
English version:
Theoretical and Mathematical Physics, 1992, Volume 93, Issue 1, Pages 1081–1090
DOI: https://doi.org/10.1007/BF01016465
Bibliographic databases:
Language: Russian
Citation: I. M. Lutsenko, “Jacobi algebra and potentials generated by it”, TMF, 93:1 (1992), 3–16; Theoret. and Math. Phys., 93:1 (1992), 1081–1090
Citation in format AMSBIB
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\by I.~M.~Lutsenko
\paper Jacobi algebra and potentials generated by it
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\pages 3--16
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\zmath{https://zbmath.org/?q=an:0803.46085}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 93
\issue 1
\pages 1081--1090
\crossref{https://doi.org/10.1007/BF01016465}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992LF86000001}
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  • https://www.mathnet.ru/eng/tmf/v93/i1/p3
    • This publication is cited in the following 5 articles:
    1. Shakir. M. Nagiyev, C. Aydin, A. I. Ahmadov, Sh. A. Amirova, “Exactly solvable model of the linear harmonic oscillator with a position-dependent mass under external homogeneous gravitational field”, Eur. Phys. J. Plus, 137:5 (2022)  crossref
    2. A. N. Lavrenov, I. A. Lavrenov, “Howe duality of Higgs – Hahn algebra for 8D harmonic oscillator”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 55:2 (2019), 216  crossref
    3. A.V. Shapovalov, I.V. Shirokov, “Functional Algebras and Dimensional Reduction in the LPDEs Integration Problem”, JNMP, 4:1-2 (1997), 62  crossref
    4. A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration method for linear partial differential equations. Functional algebras and dimensional reduction”, Theoret. and Math. Phys., 106:1 (1996), 1–10  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, Theoret. and Math. Phys., 104:2 (1995), 921–934  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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