The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation

 Access to full text

 Full (PDF)

1. [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. Zbl0607.35070MR839284
2. [2] K. Yajima, The quasi-classical limit of scattering amplitude. I. Finite range potentials, Preprint, Tokyo, 1984. Zbl0591.35079
3. [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. [4] K. Yajima, The quasi-classical limit of scattering amplitude. L2-approach for short range potentials, Preprint, Wien, 1984. 
5. [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). MR613721
6. [6] L.D. Landau, E.M. Lifshitz, The quantum mechanics, Moscow, Fizmatgiz, 1963 (Russian). Zbl0081.22207
7. [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). Zbl0588.47011MR821483
8. [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. Zbl0415.47006MR541355
9. [9] V. Enss, B. Simon, Finite total cross sections in nonrelativistic quantum mechanics, Commun. Math. Phys., t. 76, 1980, p. 177-209. Zbl0471.35065MR587510
10. [10] D.R. Yafaev, On the resonant scattering by a negative potential, Notes of LOMI Sci. Seminars, t. 138, 1984, p. 184-193 (Russian). Zbl0557.35094MR755917
11. [11] M. Reed, B. Simon, Methods of modern mathematical physics. III. Scattering theory, New York, Academic Press, 1979. Zbl0405.47007MR529429
12. [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). MR514135
13. [13] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Commun. Math. Phys., t. 78, 1981, p. 391-400. Zbl0489.47010MR603501
14. [14] P. Perry, I.M. Sigal, B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math., t. 114, 1981, p. 519-567. Zbl0477.35069MR634428
15. [15] B.R. Vainberg, Asymptotic methods in equations of mathematical physics, Moscow, MGU, 1982 (Russian). Zbl0518.35002MR700559
16. [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. Zbl0561.35021MR755930

1. D. R. Yafaev, On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
2. D. R. Yafaev, On the scattering matrix for perturbations of constant sign
3. Shu Nakamura, Scattering theory for the shape resonance model. I. Non-resonant energies
4. Évelyne Latrémolière, Opérateur de Schrödinger avec une métrique
5. Didier Robert, Hideo Tamura, Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections
6. Peter D. Hislop, Shu Nakamura, Semiclassical resolvent estimates