Geodesic
Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 211-222 
V. S. Ol'khovskii. Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 211-222. http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a7/
@article{TMF_1974_20_2_a7,
     author = {V. S. Ol'khovskii},
     title = {Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {211--222},
     year = {1974},
     volume = {20},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a7/}
}
TY  - JOUR
AU  - V. S. Ol'khovskii
TI  - Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1974
SP  - 211
EP  - 222
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a7/
LA  - ru
ID  - TMF_1974_20_2_a7
ER  - 
%0 Journal Article
%A V. S. Ol'khovskii
%T Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1974
%P 211-222
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a7/
%G ru
%F TMF_1974_20_2_a7

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

A study is made of the general properties of the one-charmei unitary and non-unitary $S$-matrix in the case when the interaction inside a sphere of finite radius is unknown while outside the sphere there is a centrifugal barrier plus a noaasingular potential “tail” that decreases asymptotically not weaker than exponentially. Use is made of the completeness condition of a solution of the Schrödinger equation outside the sphere of unknown interaction, symmetry, and generalized unitarity of the $S$-matrix. As illustration, the concrete example of the resonance behavior of scattering and absorption cross sections is studied; this generalizes the well-known results in model exposition. In addition, the fulfilment of the orthodox conditions of micro- and macrocausality for the final results is investigated.

[1] N. Van Kampen, Phys. Rev., 91 (1953), 1267 ; Problemy sovremennoi fiziki, no. 2, 1957, 44 | DOI | MR | Zbl

[2] I. Saavedra, Nucl. Phys., 29 (1962), 137 ; 87 (1966), 267 | DOI | MR | Zbl | DOI | MR

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

[4] V. de Alfaro, T. Redzhe, Potentsialnoe rasseyanie, «Mir», 1966 | Zbl

[5] W. Heisenberg, Z. Naturforsch., 1 (1946), 608 | MR | Zbl

[6] Hu Ning, Phys. Rev., 74 (1948), 131 | DOI | Zbl

[7] V. S. Olkhovskii, Yu. V. Tsekhmistrenko, Ukr. fiz. zhurn., 6 (1961), 149

[8] M. G. Gasymov, DAN SSSR, 165 (1965), 261 | MR | Zbl

[9] M. Bertero et al., Nuovo Cim., 2A (1971), 1024 | DOI | MR

[10] E. Titchmarsh, Teoriya funktsii, GITTL, 1951 | MR

[11] A. S. Davydov, Teoriya atomnogo yadra, Fizmatgiz, 1958

[12] T. Ohmura, Progr. Theor. Phys., Suppl., 1964, no. 29, 108 | DOI | MR | Zbl

[13] V. S. Olkhovsky, Nuovo Cim., 4A (1971), 605 | DOI

[14] V. S. Olkhovsky, E. Recami, Nuovo Cim., 63A (1969), 814 | DOI