Phase-shift method for scattering on potentials that allow separation of variables in spheroidal coordinates
Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 2, pp. 253-259 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that angular functions arising in the separation of variables as well as the phases of corresponding radial functions represent the eigen-functions and phases of the unitary operator $SI$. The scattering amplitude and cross-sections are directly expressed in terms of these functions and phase shifts. Modified expansion for the amplitude is suggested for long-range potentials with the Coulomb behaviour at large distances.
@article{TMF_1975_22_2_a10,
     author = {D. I. Abramov and I. V. Komarov},
     title = {Phase-shift method for scattering on potentials that allow separation of variables in spheroidal coordinates},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {253--259},
     year = {1975},
     volume = {22},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_22_2_a10/}
}
TY  - JOUR
AU  - D. I. Abramov
AU  - I. V. Komarov
TI  - Phase-shift method for scattering on potentials that allow separation of variables in spheroidal coordinates
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1975
SP  - 253
EP  - 259
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1975_22_2_a10/
LA  - ru
ID  - TMF_1975_22_2_a10
ER  - 
%0 Journal Article
%A D. I. Abramov
%A I. V. Komarov
%T Phase-shift method for scattering on potentials that allow separation of variables in spheroidal coordinates
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1975
%P 253-259
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1975_22_2_a10/
%G ru
%F TMF_1975_22_2_a10
D. I. Abramov; I. V. Komarov. Phase-shift method for scattering on potentials that allow separation of variables in spheroidal coordinates. Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 2, pp. 253-259. http://geodesic.mathdoc.fr/item/TMF_1975_22_2_a10/

[1] B. Moisevich, Atomnye i molekulyarnye protsessy, «Mir», 1964, 254

[2] K. Flammer, Tablitsy volnovykh sferoidalnykh funktsii, Izd-vo VTs AN SSSR, 1962 | MR

[3] M. Shimizu, J. Phys. Soc. Japan, 18 (1963), 811 | DOI

[4] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatgiz, 1963

[5] D. I. Abramov, I. V. Komarov, Abstracts of papers VIII ICPEAC, 1, Beograd, 1973, 376

[6] Yu. N. Demkov, V. S. Rudakov, ZhETF, 59 (1970), 2035

[7] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. 3, «Nauka», 1965 | MR

[8] I. Lukach, Ya. A. Smorodinskii, TMF, 14 (170), 1973

[9] I. Lukach, TMF, 14 (1973), 366

[10] A. I. Shum, Matem. sbornik, 47 (1959), 495 | Zbl

[11] R. Nyuton, Teoriya rasseyaniya voln i chastits, «Mir», 1969 | MR