
This article is cited in 2 scientific papers (total in 2 papers)
Perturbation theory for onedimensional 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 eigenfunctions and eigenvalues 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.
Full text:
PDF file (498 kB)
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 1971, 9:3, 1256–1258
Received: 06.04.1971
Citation:
V. S. Pekar, “Perturbation theory for onedimensional 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 onedimensional Schrodinger equations that can be used in a~region where the wave function is small
\jour TMF
\yr 1971
\vol 9
\issue 3
\pages 440444
\mathnet{http://mi.mathnet.ru/tmf4517}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 9
\issue 3
\pages 12561258
\crossref{https://doi.org/10.1007/BF01043417}
Linking options:
http://mi.mathnet.ru/eng/tmf4517 http://mi.mathnet.ru/eng/tmf/v9/i3/p440
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:

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

G. V. Vikhnina, V. S. Pekar, “Excited states in logarithmic perturbation theory”, Theoret. and Math. Phys., 68:1 (1986), 740–743

Number of views: 
This page:  266  Full text:  97  References:  29  First page:  1 
