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 TMF, 1996, Volume 106, Number 2, Pages 273–284 (Mi tmf1113)

Local symmetry algebra of Shrödinger equation for Hydrogen atom

A. A. Drokina, A. V. Shapovalova, I. V. Shirokovb

a Tomsk State University
b Omsk State University

Abstract: The complete description of local symmetries (which are differential operators of arbitrary finite order) is given for stationary Shrödinger equation for Hydrogen atom. This is done using the reduction of Shrödinger equation for isotropic harmonic oscillator to one for the Hydrogen atom, which induces the correspondent symmetry algebras reduction. It is shown that all nontrivial local symmetry operators for $n$-dimensional isotropic harmonic oscillator belong to enveloping algebra $U(su(n,C))$ of algebra $su(n,C)$. For Hydrogen atom all nontrivial local symmetries constitute enveloping algebra $U(so(4,C))$ of algebra $so(4,C)$. Basis of $so(4,C)$ consists of rotation group generators and Runge–Lenz-operators.

DOI: https://doi.org/10.4213/tmf1113

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English version:
Theoretical and Mathematical Physics, 1996, 106:2, 227–236

Bibliographic databases:

Citation: A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Local symmetry algebra of Shrödinger equation for Hydrogen atom”, TMF, 106:2 (1996), 273–284; Theoret. and Math. Phys., 106:2 (1996), 227–236

Citation in format AMSBIB
\Bibitem{DroShaShi96} \by A.~A.~Drokin, A.~V.~Shapovalov, I.~V.~Shirokov \paper Local symmetry algebra of Shr\"odinger equation for Hydrogen atom \jour TMF \yr 1996 \vol 106 \issue 2 \pages 273--284 \mathnet{http://mi.mathnet.ru/tmf1113} \crossref{https://doi.org/10.4213/tmf1113} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1402010} \zmath{https://zbmath.org/?q=an:0889.35083} \transl \jour Theoret. and Math. Phys. \yr 1996 \vol 106 \issue 2 \pages 227--236 \crossref{https://doi.org/10.1007/BF02071077} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996VN51500008}