Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections

Didier Robert; Hideo Tamura

Annales de l'I.H.P. Physique théorique (1987)

  • Volume: 46, Issue: 4, page 415-442
  • ISSN: 0246-0211

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Robert, Didier, and Tamura, Hideo. "Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections." Annales de l'I.H.P. Physique théorique 46.4 (1987): 415-442. <http://eudml.org/doc/76367>.

@article{Robert1987,
author = {Robert, Didier, Tamura, Hideo},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {semi-classical estimates; resolvent; Schrödinger operator; commutator method; total scattering cross-sections},
language = {eng},
number = {4},
pages = {415-442},
publisher = {Gauthier-Villars},
title = {Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections},
url = {http://eudml.org/doc/76367},
volume = {46},
year = {1987},
}

TY - JOUR
AU - Robert, Didier
AU - Tamura, Hideo
TI - Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections
JO - Annales de l'I.H.P. Physique théorique
PY - 1987
PB - Gauthier-Villars
VL - 46
IS - 4
SP - 415
EP - 442
LA - eng
KW - semi-classical estimates; resolvent; Schrödinger operator; commutator method; total scattering cross-sections
UR - http://eudml.org/doc/76367
ER -

References

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  5. [5] H. Isozaki and H. Kitada, Modified wave operators with time-independent modifiers. J. Fac. Sci. Univ. Tokyo Sect. IA, Math., t. 32, 1985, p. 77-104. Zbl0582.35036MR783182
  6. [6] H. Kitada and K. Yajima, A scattering theory for time-dependent long-range potentials. Duke Math. J., t. 49, 1982, p. 341-376. Zbl0499.35087MR659945
  7. [7] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators. Comm. Math. Phys., t. 78, 1981, p. 391-408. Zbl0489.47010MR603501
  8. [8] M. Murata, High energy resolvent estimates I, first order operators, and II, higher order elliptic operators. J. Math. Soc. Japan, t. 35, 1983, p. 711-733, and t. 36, 1984, p. 1-10. Zbl0513.35010MR714471
  9. [9] P. Perry, I.M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators. Ann. of Math., t. 114, 1981, p. 519-567. Zbl0477.35069MR634428
  10. [10] M. Reed and B. Simon, Methods of modern mathematical physics, III, Scattering theory, Academic Press, 1979. Zbl0405.47007MR529429
  11. [11] D. Robert, Autour de l'approximation semi-classique. Notas de Curso. Instituto de Math., no 21, Recife, 1983 et PM 68, Birkhaüser, 1987. Zbl0621.35001MR897108
  12. [12] D. Robert and H. Tamura, Semi-classical bounds for resolvents of Schrödinger operators and asymptotics for scattering phases. Comm. Partial Differ. Equ., t. 9, 1984, p. 1017-1058. Zbl0561.35021MR755930
  13. [13] A.V. Sobolev and D.R. Yafaev, On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics. Ann. Inst. Henri Poincaré, t. 44, 1986, p. 195-210. Zbl0607.35070MR839284
  14. [14] B.R. Vainberg, On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t → ∞ of solutions of non-stationary problems. Russian Math. Surveys, t. 30, 1975, p. 1-58. Zbl0318.35006MR415085
  15. [15] B.R. Vainberg, Quasi-classical approximation in stationary scattering problems. Func. Anal. Appl., t. 11, 1977, p. 6-18. Zbl0381.35022
  16. [16] D.R. Yafaev, The eikonal approximation and the asymptotics of the total cross–section for the Schrödinger equation. Ann. Inst. Henri Poincaré, t. 44, 1986, p. 397- 425. Zbl0608.35054MR850898
  17. [17] K. Yajima, The quasi-classical limit of scattering amplitude - finite range potentials—. Lecture Notes in Math., 1159, Springer, 1984. Zbl0591.35079MR824991
  18. [18] K. Yajima, The quasi-classical limit of scattering amplitude - L2 approach for short range potentials —, Preprint, 1985. MR824991

Citations in EuDML Documents

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  1. Didier Robert, H. Tamura, Limite semi-classique de l'amplitude de diffusion
  2. X. P. Wang, Sections efficaces dans le problème à N -corps
  3. D. R. Yafaev, On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
  4. Christian Gérard, Semiclassical resolvent estimates for two and three-body Schrödinger operators
  5. Hideo Tamura, Shadow scattering by magnetic fields in two dimensions
  6. Shu Nakamura, Scattering theory for the shape resonance model. I. Non-resonant energies
  7. Xue-Ping Wang, Time-decay of scattering solutions and classical trajectories
  8. Th. Jecko, Classical limit of elastic scattering operator of a diatomic molecule in the Born-Oppenheimer approximation
  9. Évelyne Latrémolière, Opérateur de Schrödinger avec une métrique
  10. Didier Robert, H. Tamura, Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits

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