Geodesic
Cook's method in the problem of the many-body Coulomb wave operator convergence
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 2, pp. 559-566.

Voir la notice de l'article provenant de la source Math-Net.Ru

The present work is devoted to the problem of existence of the Coulomb wave operator. Two- and three-body quantum systems of charged particles are under investigation. Using the effective charge technique we show that there exists a number of equivalent integral equations for the three charged particles scattering wave operator. 
@article{FPM_2002_8_2_a11,
     author = {V. L. Shablov and V. A. Bilyk and Yu. V. Popov},
     title = {Cook's method in the problem of the many-body {Coulomb} wave operator convergence},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {559--566},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_2_a11/}
}
TY  - JOUR
AU  - V. L. Shablov
AU  - V. A. Bilyk
AU  - Yu. V. Popov
TI  - Cook's method in the problem of the many-body Coulomb wave operator convergence
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 559
EP  - 566
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_2_a11/
LA  - ru
ID  - FPM_2002_8_2_a11
ER  - 
%0 Journal Article
%A V. L. Shablov
%A V. A. Bilyk
%A Yu. V. Popov
%T Cook's method in the problem of the many-body Coulomb wave operator convergence
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 559-566
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_2_a11/
%G ru
%F FPM_2002_8_2_a11
V. L. Shablov; V. A. Bilyk; Yu. V. Popov. Cook's method in the problem of the many-body Coulomb wave operator convergence. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 2, pp. 559-566. http://geodesic.mathdoc.fr/item/FPM_2002_8_2_a11/

[1] Muhlerin D., Zinnes I. I., “Coulomb scattering. I: Single channel”, J. Math. Phys., 11 (1970), 1402–1408 | DOI | MR

[2] Chandler C., Gibson A. G., “Time-dependent multichannel Coulomb scattering theory”, J. Math. Phys., 15 (1974), 291–294 | DOI | MR

[3] Chandler C., Nucl. Phys. A, 353 (1981), 129 | DOI

[4] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 3. Teoriya rasseyaniya, Mir, M., 1982 | MR

[5] Teilor Dzh., Teoriya rasseyaniya, Mir, M., 1985 | MR

[6] Komarov V. V., Popova A. M., Shablov V. L., Dinamika sistem neskolkikh kvantovykh chastits, Izd-vo MGU, M., 1996

[7] Shablov V. L., Shitkov Yu. Yu., Popov Yu. V., “O svyazi statsionarnoi i nestatsionarnoi teorii rasseyaniya dlya sistemy chastits s kulonovskim vzaimodeistviem”, Fundam. i prikl. mat., 2:3 (1996), 925–951 | MR | Zbl

[8] Peterkop R. K., Teoriya ionizatsii atomov elektronnym udarom, Zinatne, Riga, 1975

[9] Dollard J. D., “Asymptotic convergence and the Coulomb interaction”, J. Math. Phys., 5 (1964), 729–738 | DOI | MR

[10] Shablov V. L., Bilyk V. A., Popov Yu. V., “Metod rezolventnykh integralnykh uravnenii v zadache o rasseyanii trekh chastits s kulonovskim vzaimodeistviem”, Fundam. i prikl. mat., 4:4 (1998), 1207–1224 | MR | Zbl

[11] Brauner M., Briggs J. S., Klar H., J. Math. Phys., 22 (1989), 2265 | DOI

[12] Merkurev S. P., Voprosy teorii atomnykh stolknovenii, Vyp. 2, Izd-vo LGU, L., 1980