The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation
Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 4, pp. 397-425.
@article{AIHPA_1986__44_4_397_0,
     author = {Yafaev, Dimitri},
     title = {The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schr\"odinger equation},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {397--425},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {4},
     year = {1986},
     zbl = {0608.35054},
     mrnumber = {850898},
     language = {en},
     url = {www.numdam.org/item/AIHPA_1986__44_4_397_0/}
}
Yafaev, D. R. The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation. Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 4, pp. 397-425. http://www.numdam.org/item/AIHPA_1986__44_4_397_0/

[1] A.V. Sobolev, D.R. Yafaev, On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics, Annales de l'I. H. P., t. 44, n° 2, 1986, p. 195-210. | Numdam | MR 839284 | Zbl 0607.35070

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

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

[4] K. Yajima, The quasi-classical limit of scattering amplitude. L2-approach for short range potentials, Preprint, Wien, 1984.

[5] M.Sh. Birman, D.R. Yafaev, The asymptotics of the spectrum of S-matrix by potential scattering, Soviet Math. Dokl., t. 255, n° 5, 1980, p. 1085-1087 (Russian). | MR 613721

[6] L.D. Landau, E.M. Lifshitz, The quantum mechanics, Moscow, Fizmatgiz, 1963 (Russian).

[7] A.V. Sobolev, D.R. Yafaev, Phase analysis in the problem of scattering by a radial potential, Notes of LOMI Sci. Seminars, t. 147, 1985, p. 155-178 (Russian). | MR 821483 | Zbl 0588.47011

[8] W. Amrein, O. Pearson, A time-dependent approach to the total scattering cross-section. J. Phys. A : Math. Gen., t. 12, n° 4, 1979, p. 1469-1492. | MR 541355 | Zbl 0415.47006

[9] V. Enss, B. Simon, Finite total cross sections in nonrelativistic quantum mechanics, Commun. Math. Phys., t. 76, 1980, p. 177-209. | MR 587510 | Zbl 0471.35065

[10] D.R. Yafaev, On the resonant scattering by a negative potential, Notes of LOMI Sci. Seminars, t. 138, 1984, p. 184-193 (Russian). | MR 755917 | Zbl 0557.35094

[11] M. Reed, B. Simon, Methods of modern mathematical physics. III. Scattering theory, New York, Academic Press, 1979. | MR 529429 | Zbl 0405.47007

[12] D.R. Yafaev, On the theory of multichannel scattering in a pair of spaces, Teor. Mat. Fiz., t. 37, n° 1, 1978, p. 48-57 (Russian). | MR 514135

[13] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Commun. Math. Phys., t. 78, 1981, p. 391-400. | MR 603501 | Zbl 0489.47010

[14] P. Perry, I.M. Sigal, B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math., t. 114, 1981, p. 519-567. | MR 634428 | Zbl 0477.35069

[15] B.R. Vainberg, Asymptotic methods in equations of mathematical physics, Moscow, MGU, 1982 (Russian). | MR 700559

[16] D. Robert, H. Tamura, Semi-classical bounds for resolvents of Schrödinger operators and asymptotics for scattering phases, Comm. in PDE, t. 9 (10), 1984, p. 1017-1058. | MR 755930 | Zbl 0561.35021