On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics

A. V. Sobolev; D. R. Yafaev

Annales de l'I.H.P. Physique théorique (1986)

  • Volume: 44, Issue: 2, page 195-210
  • ISSN: 0246-0211

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Sobolev, A. V., and 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 44.2 (1986): 195-210. <http://eudml.org/doc/76317>.

@article{Sobolev1986,
author = {Sobolev, A. V., Yafaev, D. R.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {quasi-classical limit; scattering cross-section; Schrödinger equation; radial potential},
language = {eng},
number = {2},
pages = {195-210},
publisher = {Gauthier-Villars},
title = {On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics},
url = {http://eudml.org/doc/76317},
volume = {44},
year = {1986},
}

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
PB - Gauthier-Villars
VL - 44
IS - 2
SP - 195
EP - 210
LA - eng
KW - quasi-classical limit; scattering cross-section; Schrödinger equation; radial potential
UR - http://eudml.org/doc/76317
ER -

References

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  1. [1] L.D. Landau, E.M. Lifshitz, Quantum mechanics, Moscow, Fizmatgiz, 1963 (Russian). Zbl0081.22207
  2. [2] W. Hunziker, Potential scattering at high energies, Helv. Phys. Acta, t. 36, 1963, p. 838-858. MR180135
  3. [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). Zbl0203.13403MR205110
  4. [4] A. Jensen, The scattering cross-section and its Born approximation at high energies, Helv. Phys. Acta, t. 53, 1980, p. 398-403. MR611766
  5. [5] K. Yajima, The quasi-classical limit of scattering amplitude I. Finite range potentials. Preprint. Tokyo, 1984. Zbl0591.35079
  6. [6] D.R. Yafaev, The eikonal approximation for the Schrödinger equation, Uspehi Mat. Nauk, t. 40, n° 5, 1985, p. 240 (Russian). Zbl0693.35125
  7. [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. Zbl0415.47006MR541355
  8. [8] V. Enss, B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics, Commun. Math. Phys., t. 76, 1980, p. 177-209. Zbl0471.35065MR587510
  9. [9] D.R. Yafaev, On the resonant scattering by a negative potential, Notes of Lomi seminars, t. 138, 1984, p. 184-193 (Russian). Zbl0557.35094MR755917
  10. [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). MR613721
  11. [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). Zbl0588.47011MR821483
  12. [12] A.I. Baz, A.M. Perelomov, Ya.B. Zeldovitch, Scattering, reactions and decay in nonrelativistic quantum mechanics, Moscow, Nauka, 1971 (Russian). 
  13. [13] F. Calogero, Variable phase approach to potential scattering, New York, London, Academic Press, 1967. Zbl0193.57501
  14. [14] M. Abromowitz, I.A. Stegun, Handbook of mathematical functions, Dover Inc., 1972. 
  15. [15] I.C. Gohberg, M.G. Krein, Introduction à la théorie des opérateurs linéaires non auto-adjoints dans un espace hilbertien, Paris, Dunod, 1971. MR350445
  16. [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). Zbl0196.45004MR139007

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