On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 2, pp. 195-210.
@article{AIHPA_1986__44_2_195_0,
     author = {Sobolev, A. V. and Yafaev, D. R.},
     title = {On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {195--210},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {2},
     year = {1986},
     mrnumber = {839284},
     zbl = {0607.35070},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1986__44_2_195_0/}
}
TY  - JOUR
AU  - Sobolev, A. V.
AU  - Yafaev, D. R.
TI  - On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1986
SP  - 195
EP  - 210
VL  - 44
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1986__44_2_195_0/
LA  - en
ID  - AIHPA_1986__44_2_195_0
ER  - 
%0 Journal Article
%A Sobolev, A. V.
%A Yafaev, D. R.
%T On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
%J Annales de l'I.H.P. Physique théorique
%D 1986
%P 195-210
%V 44
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1986__44_2_195_0/
%G en
%F AIHPA_1986__44_2_195_0
Sobolev, A. V.; Yafaev, D. R. On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics. Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 2, pp. 195-210. http://www.numdam.org/item/AIHPA_1986__44_2_195_0/

[1] L.D. Landau, E.M. Lifshitz, Quantum mechanics, Moscow, Fizmatgiz, 1963 (Russian).

[2] W. Hunziker, Potential scattering at high energies, Helv. Phys. Acta, t. 36, 1963, p. 838-858. | MR

[3] V.S. Buslaev, Trace formulae and some asymptotic estimates of the resolvent kernel for the three-dimensional Schrödinger operator, Topics in Math. Physics, t. 1, 1966, p. 82-101 (Russian). | MR | Zbl

[4] A. Jensen, The scattering cross-section and its Born approximation at high energies, Helv. Phys. Acta, t. 53, 1980, p. 398-403. | MR

[5] K. Yajima, The quasi-classical limit of scattering amplitude I. Finite range potentials. Preprint. Tokyo, 1984. | Zbl

[6] D.R. Yafaev, The eikonal approximation for the Schrödinger equation, Uspehi Mat. Nauk, t. 40, n° 5, 1985, p. 240 (Russian).

[7] W. Amrein, O. Pearson, A time-dependent approach to the total scattering cross-section, J. Phys. A : Math. Gen., t. 12, 1979, p. 1469-1492. | MR | Zbl

[8] V. Enss, B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics, Commun. Math. Phys., t. 76, 1980, p. 177-209. | MR | Zbl

[9] D.R. Yafaev, On the resonant scattering by a negative potential, Notes of Lomi seminars, t. 138, 1984, p. 184-193 (Russian). | MR | Zbl

[10] M.Sh. Birman, D.R. Yafaev, The asymptotics of the spectrum of the s-matrix by a potential scattering, Dokl. Acad. Nauk USSR, t. 255, 1980, p. 1085-1087 (Russian). | MR

[11] A.V. Sobolev, D.R. Yafaev, Phase analysis for scattering by a radial potential, Notes of Lomi seminars, t. 147, 1985, p. 155-178 (Russian). | MR | Zbl

[12] A.I. Baz, A.M. Perelomov, Ya.B. Zeldovitch, Scattering, reactions and decay in nonrelativistic quantum mechanics, Moscow, Nauka, 1971 (Russian).

[13] F. Calogero, Variable phase approach to potential scattering, New York, London, Academic Press, 1967. | Zbl

[14] M. Abromowitz, I.A. Stegun, Handbook of mathematical functions, Dover Inc., 1972.

[15] I.C. Gohberg, M.G. Krein, Introduction à la théorie des opérateurs linéaires non auto-adjoints dans un espace hilbertien, Paris, Dunod, 1971. | MR

[16] M.Sh. Birman, M.G. Krein, On the theory of wave operators and scattering operators, Dokl. Acad. Nauk. USSR, t. 144, 1962, p. 475-478 (Russian). | MR | Zbl