Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 440-444
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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.
@article{TMF_1971_9_3_a13,
author = {V. S. Pekar},
title = {Perturbation theory for one-dimensional {Schrodinger} equations that can be used in a~region where the wave function is small},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {440--444},
year = {1971},
volume = {9},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a13/}
}
TY - JOUR AU - V. S. Pekar TI - Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1971 SP - 440 EP - 444 VL - 9 IS - 3 UR - http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a13/ LA - ru ID - TMF_1971_9_3_a13 ER -
%0 Journal Article %A V. S. Pekar %T Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small %J Teoretičeskaâ i matematičeskaâ fizika %D 1971 %P 440-444 %V 9 %N 3 %U http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a13/ %G ru %F TMF_1971_9_3_a13
V. S. Pekar. Perturbation theory for one-dimensional Schrodinger equations that can be used in a region where the wave function is small. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 440-444. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a13/
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