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 SIGMA, 2012, Volume 8, 060, 15 pages (Mi sigma737)

Ladder operators for quantum systems confined by dihedral angles

Eugenio Ley-Kooa, Guo-Hua Sunb

a Instituto de Física, Universidad Nacional Autónoma de México, México
b Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, México

Abstract: We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relationships between the eigenfunctions in each pair of coordinates, and with the same eigenenergies are also illustrated.

Keywords: Ladder operators; harmonic oscillator; hydrogen atom; confinement in dihedral angles.

DOI: https://doi.org/10.3842/SIGMA.2012.060

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ArXiv: 1209.2497
MSC: 20C35; 33C47; 35J15; 35J25; 81Q05; 81R05
Received: June 29, 2012; in final form September 7, 2012; Published online September 12, 2012
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Citation: Eugenio Ley-Koo, Guo-Hua Sun, “Ladder operators for quantum systems confined by dihedral angles”, SIGMA, 8 (2012), 060, 15 pp.

Citation in format AMSBIB
\Bibitem{LeySun12} \by Eugenio Ley-Koo, Guo-Hua Sun \paper Ladder operators for quantum systems confined by dihedral angles \jour SIGMA \yr 2012 \vol 8 \papernumber 060 \totalpages 15 \mathnet{http://mi.mathnet.ru/sigma737} \crossref{https://doi.org/10.3842/SIGMA.2012.060} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2970768} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000308736900001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867018311} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Ricardo Méndez-Fragoso, Eugenio Ley-Koo, “Ladder operators for Lamé spheroconal harmonic polynomials”, SIGMA, 8 (2012), 074, 16 pp.
2. Eugenio Ley-Koo, Guo-Hua Sun, “Surface Effects in the Hydrogen Atom Confined by Dihedral Angles”, Electronic Structure of Quantum Confined Atoms and Molecules, 2014, 1–29
3. Cruz S.A., Ley-Koo E., “the Hydrogen H-2(+) and Heh2+ Molecular Ions Confined in Dihedral Angles”, Concepts of Mathematical Physics in Chemistry: a Tribute To Frank E. Harris - Pt a, Adv. Quantum Chem., 71, eds. Sabin J., CabreraTrujillo R., Elsevier Academic Press Inc, 2015, 69–113
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