Geodesic
Reformulation of the Lax–Phillips approach in terms of stationary scattering theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 248-265 
A. K. Motovilov. Reformulation of the Lax–Phillips approach in terms of stationary scattering theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 2, pp. 248-265. http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/
@article{TMF_1994_98_2_a6,
     author = {A. K. Motovilov},
     title = {Reformulation of the {Lax{\textendash}Phillips} approach in terms of stationary scattering theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {248--265},
     year = {1994},
     volume = {98},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/}
}
TY  - JOUR
AU  - A. K. Motovilov
TI  - Reformulation of the Lax–Phillips approach in terms of stationary scattering theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 248
EP  - 265
VL  - 98
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/
LA  - ru
ID  - TMF_1994_98_2_a6
ER  - 
%0 Journal Article
%A A. K. Motovilov
%T Reformulation of the Lax–Phillips approach in terms of stationary scattering theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 248-265
%V 98
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1994_98_2_a6/
%G ru
%F TMF_1994_98_2_a6

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

The Lax–Phillips approach for the Schrödinger equation is reformulated in terms of $t$ and $s$-matrices from stationary scattering theory. New proofs of the incoming and outgoing subspaces orthogonality and analytic continuability of the resolvents on the non-physycal sheet are given. The obtained results are generated to the case of multichannel Hamiltonians for analytic continuation on the non-physical sheet which is connected with the physical one by crossing through the interval between lower thresholds.

[1] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971 | MR

[2] Nyuton R., Teoriya rasseyaniya voln i chastits, Mir, M., 1969 | MR

[3] Merkurev S. P., Faddeev L. D., Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR

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

[5] Brandas E., Elander N.(eds.), Resonances, Springer-Verlag, 1987 | MR

[6] Meller K., Orlov Yu. V., EChAYa, 20:6 (1989), 1341–1395

[7] Faddeev L. D., Tr. MIAN SSSR, 69, 1963, 1–122 | MR | Zbl

[8] Pavlov B. S., Int. Workshop “Math. Aspects of the Scattering Theory and Applications” (SPb, 20–24.05.91), 113–124

[9] Pavlov B. C., Fedorov S. I., Algebra i analiz, 1:2 (1989), 132–168 | MR | Zbl

[10] Fedorov S. I., Matem. sb., 181:6 (1990), 833–864 | MR

[11] Laks P., Fillips R., Teoriya rasseyaniya dlya avtomorfnykh funktsii, Mir, M., 1979

[12] Gelfand I. M., Shilov G. E., Prostranstva osnovnykh i obobschennykh funktsii, t. 1, Fizmatgiz, M., 1958 | MR