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

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

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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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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
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
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