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TMF, 1971, Volume 9, Number 3, Pages 440–444 (Mi tmf4517)  

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

Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small

V. S. Pekar


Abstract: The usual perturbation theory series converges badly in the region where the wavefunction $\psi$ is small and the relative correction to $\psi$ is great. The new simple perturbation method is proposed, which is valid, in particular, in the region where $\psi$ is small. The method is based on expanding in the perturbation theory series not the function $\psi$ itself, but its logarithmic derivative,$\frac{d}{dx}\ln\psi$. Corrections of any order to eigen-functions and eigen-values are expressed in quadratures instead of infinite seria. The examples are considered which demonstrate the rapid convergence of the method proposed in cases when the series of the usual theory converges badly.

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English version:
Theoretical and Mathematical Physics, 1971, 9:3, 1256–1258

Received: 06.04.1971

Citation: V. S. Pekar, “Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small”, TMF, 9:3 (1971), 440–444; Theoret. and Math. Phys., 9:3 (1971), 1256–1258

Citation in format AMSBIB
\Bibitem{Pek71}
\by V.~S.~Pekar
\paper Perturbation theory for one-dimensional Schrodinger equations that can be used in a~region where the wave function is small
\jour TMF
\yr 1971
\vol 9
\issue 3
\pages 440--444
\mathnet{http://mi.mathnet.ru/tmf4517}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 9
\issue 3
\pages 1256--1258
\crossref{https://doi.org/10.1007/BF01043417}


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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. V. S. Polikanov, “On a rapidly converging perturbation theory for a discrete spectrum”, Theoret. and Math. Phys., 24:2 (1975), 794–798  mathnet  crossref  mathscinet  zmath
    2. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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