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SIGMA, 2012, Volume 8, 063, 14 pages (Mi sigma740)  

This article is cited in 4 scientific papers (total in 4 papers)

Singular isotonic oscillator, supersymmetry and superintegrability

Ian Marquette

School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia

Abstract: In the case of a one-dimensional nonsingular Hamiltonian $H$ and a singular supersymmetric partner $H_{a}$, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions.

Keywords: supersymmetric quantum mechanics; superintegrability; isotonic oscillator; polynomial algebra; special functions.

DOI: https://doi.org/10.3842/SIGMA.2012.063

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Full text: http://emis.mi.ras.ru/.../063
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Bibliographic databases:

ArXiv: 1209.4151
MSC: 81R15; 81R12; 81R50
Received: July 20, 2012; in final form September 14, 2012; Published online September 19, 2012
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Citation: Ian Marquette, “Singular isotonic oscillator, supersymmetry and superintegrability”, SIGMA, 8 (2012), 063, 14 pp.

Citation in format AMSBIB
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\paper Singular isotonic oscillator, supersymmetry and superintegrability
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Grandati Y., “A Short Proof of the Gaillard-Matveev Theorem Based on Shape Invariance Arguments”, Phys. Lett. A, 378:26-27 (2014), 1755–1759  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Ioffe M.V. Kolevatova E.V. Nishnianidze D.N., “SUSY method for the three-dimensional Schrödinger equation with effective mass”, Phys. Lett. A, 380:41 (2016), 3349–3354  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. S. Plyushchay, “Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis”, Ann. Phys., 377 (2017), 164–179  crossref  mathscinet  zmath  isi  scopus
    4. C D. J. Fernandez, V. Said Morales-Salgado, “Higher order supersymmetric truncated oscillators”, Ann. Phys., 388 (2018), 122–134  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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