Geodesic
About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object
Matematičeskoe modelirovanie, Tome 22 (2010) no. 2, pp. 83-92 
E. A. Vedutenko; S. V. Talalov. About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object. Matematičeskoe modelirovanie, Tome 22 (2010) no. 2, pp. 83-92. http://geodesic.mathdoc.fr/item/MM_2010_22_2_a5/
@article{MM_2010_22_2_a5,
     author = {E. A. Vedutenko and S. V. Talalov},
     title = {About calculation of unperturbative amplitude for the scattering of the quantum particle on a~complicated object},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--92},
     year = {2010},
     volume = {22},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_2_a5/}
}
TY  - JOUR
AU  - E. A. Vedutenko
AU  - S. V. Talalov
TI  - About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 83
EP  - 92
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_2_a5/
LA  - ru
ID  - MM_2010_22_2_a5
ER  - 
%0 Journal Article
%A E. A. Vedutenko
%A S. V. Talalov
%T About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object
%J Matematičeskoe modelirovanie
%D 2010
%P 83-92
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/MM_2010_22_2_a5/
%G ru
%F MM_2010_22_2_a5

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

We suggest a model which allows to realize a simple algorithm of numerical solution of quantum scattering problem for the neutral non-relativistic particle. The particle interacts with some quality $N\simeq10^5\div10^7$ centers which are disodered. The interval selected for number $N$ is some neighbourhood for the boundary of applying of the iterative methods for suggested scheme. The model leads to the linear algebraic system with a dimension which is 2–4 order lower than number $N$.

[1] Frank A. I., “Optika ultrakholodnykh neitronov i problema neitronnogo mikroskopa”, UFN, 121:2 (1987), 230

[2] Baz A. I., Zeldovich Ya. B., Perelomov A. M., Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, Nauka, M., 1971, 544 pp. | Zbl

[3] Berezin F., Faddeev L. D., “Zamechanie ob uravnenii Shredingera s singulyarnym potentsialom”, Doklady AN SSSR, 137:5 (1961), 1011–1014 | MR | Zbl

[4] Shirokov Yu. M., “Silno singulyarnye potentsialy v trekhmernoi kvantovoi mekhanike”, TMF, 42:1 (1980), 45–49 | MR

[5] Talalov S. V., Shirokov Yu. M., “Vzaimodeistvie zaryazhennoi chastitsy s vneshnim elektromagnitnym polem pri nalichii silno singulyarnogo potentsiala”, TMF, 46:3 (1981), 316–320 | MR

[6] Nyuton R., Teoriya rasseyaniya voln i chastits, Mir, M., 1969, 608 pp.

[7] Lifshits I. M., Gredeskul S. A., Pastur L. A., Vvedenie v teoriyu neuporyadochennykh sistem, Nauka, M., 1982, 360 pp. | MR

[8] Talalov S. V., Vedutenko E. A., “O rasseyanii massivnykh neitralnykh chastits na nanostrukturakh”, Vestnik Samarskogo gosuniversiteta, 2007, no. 9/1(59), 249–255

[9] Turchak A. I., Osnovy chislennykh metodov, Nauka, M., 1987, 320 pp. | MR | Zbl

[10] Pavlov A. S., Yukhno L. F., “O reshenii plokho obuslovlennykh lineinykh sistem iteratsionnymi metodami”, Matematicheskoe modelirovanie, 16:7 (2004), 13–20 | MR | Zbl