Problem of the $c\to\infty$ limit in the relativistic Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 2, pp. 191-196
Voir la notice de l'article provenant de la source Math-Net.Ru
A mathematical procedure is given for investigating the regular degeneration of the solutions
of the relativistic Schrödinger equation
$$
[2c\sqrt{q^2+m^2c^2}-H_0^{\operatorname{rad}}-V(r)]\Psi_{ql}(r)=0
$$
into the solutions of the nonrelativlstle equation
$$
\left[\hbar^2\frac{d^2}{dr^2}-\hbar^2\frac{l(l+1)}{r^2}-mV(r)+q^2\right]u_{ql}(r)=0
$$
for the $S$-wave case. The proposed method of a small parameter of the higher derivatives
of a differential equation is applied to several concrete problems.
@article{TMF_1970_3_2_a5,
author = {E. P. Zhidkov and V. G. Kadyshevskii and Yu. V. Katyshev},
title = {Problem of the $c\to\infty$ limit in the relativistic {Schr\"odinger} equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {191--196},
publisher = {mathdoc},
volume = {3},
number = {2},
year = {1970},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a5/}
}
TY - JOUR AU - E. P. Zhidkov AU - V. G. Kadyshevskii AU - Yu. V. Katyshev TI - Problem of the $c\to\infty$ limit in the relativistic Schr\"odinger equation JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1970 SP - 191 EP - 196 VL - 3 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a5/ LA - ru ID - TMF_1970_3_2_a5 ER -
%0 Journal Article %A E. P. Zhidkov %A V. G. Kadyshevskii %A Yu. V. Katyshev %T Problem of the $c\to\infty$ limit in the relativistic Schr\"odinger equation %J Teoretičeskaâ i matematičeskaâ fizika %D 1970 %P 191-196 %V 3 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a5/ %G ru %F TMF_1970_3_2_a5
E. P. Zhidkov; V. G. Kadyshevskii; Yu. V. Katyshev. Problem of the $c\to\infty$ limit in the relativistic Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 2, pp. 191-196. http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a5/