On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section

D. R. Yafaev

Séminaire Équations aux dérivées partielles (Polytechnique) (1988-1989)

  • page 1-10

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Yafaev, D. R.. "On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section." Séminaire Équations aux dérivées partielles (Polytechnique) (1988-1989): 1-10. <http://eudml.org/doc/111976>.

@article{Yafaev1988-1989,
author = {Yafaev, D. R.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Schrödinger equation; asymptotic formulas; total scattering cross- section; high energies; large coupling constants; scattering amplitude; linear elliptic; quasi-classical asymptotics},
language = {eng},
pages = {1-10},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section},
url = {http://eudml.org/doc/111976},
year = {1988-1989},
}

TY - JOUR
AU - Yafaev, D. R.
TI - On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1988-1989
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 10
LA - eng
KW - Schrödinger equation; asymptotic formulas; total scattering cross- section; high energies; large coupling constants; scattering amplitude; linear elliptic; quasi-classical asymptotics
UR - http://eudml.org/doc/111976
ER -

References

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  1. [Am-Pe] 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. Zbl0415.47006MR541355
  2. [Ba-Ze-Pe] A.I. Baz, Ya. B. Zeldovitch, A.M. Perelomov, Scattering, reactions and decay in nonrelativistic quantum mechanics. Moscow, Nauka, 1971 (Russian). 
  3. [Bi-Yaf] 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). MR613721
  4. [Bu] V.S. Buslaev, Trace formulas 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). Zbl0203.13403MR205110
  5. [En-Si] V. Enss, B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics. Commun. Math. Phys., t.76, 1980, p.177-209. Zbl0471.35065MR587510
  6. [Hu] W. Hunziker, Potential scattering at high energies. Helv. Phys. Acta, t.36, 1963, p.838-858. MR180135
  7. [Je] A. Jensen, The scattering cross-section and its Born approximation at high energies. Helv. Phys. Acta, t.53, 1980, p.398-403. MR611766
  8. [La-Li] L.D. Landau, E.M. Lifshitz, The quantum mechanics. Moscow, Fizmatgiz, 1963 (Russian). Zbl0081.22207
  9. [Ro-Ta,1] D. Robert, H. Tamura, Semi-classical bounds for resolvents of Schrödinger operators and asymptotics for scattering phases. Comm. in DDE, t.9 (10), 1984, p.1017-1058. Zbl0561.35021MR755930
  10. [Ro-Ta,2] D. Robert, H. Tamura, Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections. Annales de l'I.H.P., t.46, N°4, 1987, p.415-442. Zbl0648.35066MR912158
  11. [So-Yaf,1] 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
  12. [So-Yaf,2] B.R. Vainberg, Asymptotic methods in equations of mathematical physics. Moscow, MGU, 1982 (Russian). Zbl0743.35001MR700559
  13. [Yaf,1] 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
  14. [Yaf,2] D.R. Yafaev, The eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation. Annales de l'I.H.P., t.44, N°4, 1986, p.397-425. Zbl0608.35054MR850898
  15. [Yaf,3] D.R. Yafaev, The quasi-classical asymptotics of the scattering cross-section for the Schrödinger equation, Izvestija USSR Acad. Sci., ser. Math. t.52, N°1, 1988, p.139-163 (Russian). Zbl0672.35054
  16. [Yaj] K. Yajima, The quasi-classical limit of scattering amplitude-finite range potentials; Lecture Notes in math., 1159, Springer, 1984. Zbl0591.35079MR824991

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