Geodesic
Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 64-86 
V. I. Kukulin; O. A. Rubtsova. Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets). Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 64-86. http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a4/
@article{TMF_2002_130_1_a4,
     author = {V. I. Kukulin and O. A. Rubtsova},
     title = {Formulation of {Quantum} {Scattering} {Theory} in {Terms} of {Proper} {Differentials} {(Stationary} {Wave} {Packets)}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {64--86},
     year = {2002},
     volume = {130},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a4/}
}
TY  - JOUR
AU  - V. I. Kukulin
AU  - O. A. Rubtsova
TI  - Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 64
EP  - 86
VL  - 130
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a4/
LA  - ru
ID  - TMF_2002_130_1_a4
ER  - 
%0 Journal Article
%A V. I. Kukulin
%A O. A. Rubtsova
%T Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 64-86
%V 130
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a4/
%G ru
%F TMF_2002_130_1_a4

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

Constructing the basic operators of scattering theory on and off the mass shell in terms of spatially bounded stationary wave packets or proper differentials is described. For this, we use a technique based on a certain scheme for discretizing the continuum. Finite-dimensional approximations for the Green's functions and $T$-matrix, which are first found here, are immediately constructed for any energy using a single simple diagonalization of the Hamiltonian matrix in an $L_2$-type complete basis. We show that the developed approach leads to a convenient finite-dimensional representation of the scattering operators in the basis of the wave functions of a harmonic oscillator. The method allows an immediate extension to the problem of three and more bodies.

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

[2] R. Y. Rasoanaivo, G. H. Rawitscher, Phys. Rev. C, 39 (1989), 1709 | DOI

[3] A. Messia, Kvantovaya mekhanika, Nauka, M, 1978 | MR

[4] O. A. Rubtsova, V. I. Kukulin, YaF, 64 (2001), 1769

[5] O. A. Rubtsova, V. I. Kukulin, YaF, 64 (2001), 1882

[6] R. Nyuton, Teoriya rasseyaniya voln i chastits, Per. s angl., Mir, M., 1969 | MR

[7] A. M. Shirokov, Yu. F. Smirnov, TMF, 117 (1998), 227 | DOI | MR | Zbl

[8] G. F. Filippov, I. P. Okhrimenko, YaF, 32 (1980), 932; Г. Ф. Филиппов, ЯФ, 33 (1981), 928

[9] Yu. I. Nechaev, Yu. F. Smirnov, YaF, 35 (1982), 1385 | Zbl

[10] H. A. Yamani, M. S. Abdelmonem, J. Phys. B, 30 (1997), 1633 | DOI | MR

[11] H. A. Yamani, L. Fishman, J. Math. Phys., 16 (1975), 410 | DOI

[12] J. T. Broad, Phys. Rev. A, 18 (1978), 1012 | DOI | MR

[13] C. T. Corcoran, P. W. Langhoff, Math. Phys., 18(4) (1977), 651 | DOI | MR

[14] J. R. Winick, W. P. Reinhardt, Phys. Rev. A, 18 (1978), 910 | DOI

[15] I. Cacelli, V. Carravetta, A. Rizzo, J. Chem. Phys., 98 (1993), 8742 | DOI

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

[17] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR | Zbl