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TMF, 1975, Volume 24, Number 2, Pages 230–235 (Mi tmf4006)  

This article is cited in 2 scientific papers (total in 2 papers)

On a rapidly converging perturbation theory for a discrete spectrum

V. S. Polikanov


Abstract: The perturbation theory for the discrete spectrum of the radial Schrödinger equation is generalized to the case when nonperturbated function has knots. To the $k$-ih order the eigenfunction is calculated to the accuracy $\varepsilon^{2^k}$, where $\varepsilon$ is the perturbation parameter. It is possible to obtain from this eigenfunction the energy to the accuracy $\varepsilon^{2^{k+1}}$. All corrections are the quadratures of this function. The dependence on all other parts of spectrum is absent. The expressions for shiftings of the knots under the perturbation are obtained.

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English version:
Theoretical and Mathematical Physics, 1975, 24:2, 794–798

Bibliographic databases:

Received: 14.11.1974

Citation: V. S. Polikanov, “On a rapidly converging perturbation theory for a discrete spectrum”, TMF, 24:2 (1975), 230–235; Theoret. and Math. Phys., 24:2 (1975), 794–798

Citation in format AMSBIB
\Bibitem{Pol75}
\by V.~S.~Polikanov
\paper On a~rapidly converging perturbation theory for a discrete spectrum
\jour TMF
\yr 1975
\vol 24
\issue 2
\pages 230--235
\mathnet{http://mi.mathnet.ru/tmf4006}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=468810}
\zmath{https://zbmath.org/?q=an:0321.47012}
\transl
\jour Theoret. and Math. Phys.
\yr 1975
\vol 24
\issue 2
\pages 794--798
\crossref{https://doi.org/10.1007/BF01029063}


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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. G. V. Vikhnina, V. S. Pekar, “Excited states in logarithmic perturbation theory”, Theoret. and Math. Phys., 68:1 (1986), 740–743  mathnet  crossref  zmath  isi
    2. S. S. Stepanov, R. S. Tutik, “Expansion with respect to $\hbar$ for bound states of the Schrödinger equation”, Theoret. and Math. Phys., 90:2 (1992), 139–145  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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