The semiclassical limit of quantum dynamics. II : scattering theory

S. L. Robinson

Annales de l'I.H.P. Physique théorique (1988)

  • Volume: 48, Issue: 4, page 281-296
  • ISSN: 0246-0211

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Robinson, S. L.. "The semiclassical limit of quantum dynamics. II : scattering theory." Annales de l'I.H.P. Physique théorique 48.4 (1988): 281-296. <http://eudml.org/doc/76401>.

@article{Robinson1988,
author = {Robinson, S. L.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {semiclassical limit; quantum scattering; Hamiltonian; short range potentials; asymptotic behavior; compact support; Gaussian states},
language = {eng},
number = {4},
pages = {281-296},
publisher = {Gauthier-Villars},
title = {The semiclassical limit of quantum dynamics. II : scattering theory},
url = {http://eudml.org/doc/76401},
volume = {48},
year = {1988},
}

TY - JOUR
AU - Robinson, S. L.
TI - The semiclassical limit of quantum dynamics. II : scattering theory
JO - Annales de l'I.H.P. Physique théorique
PY - 1988
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 281
EP - 296
LA - eng
KW - semiclassical limit; quantum scattering; Hamiltonian; short range potentials; asymptotic behavior; compact support; Gaussian states
UR - http://eudml.org/doc/76401
ER -

References

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  2. [ES] V. Enss and B. Simon, Total cross sections in nonrelativistic scattering theory, in Quantum Mechanics in Mathematics, Chemistry and Physics, ed. My K. E. Gustafson and W. P. Reinhardt. Plenum, New York, London, 1981. 
  3. [Ha1] G.A. Hagedorn, Semiclassical quantum mechanics I: the h → 0 limit for coherent states. Commun. Math. Phys., t. 71, 1980, p. 77-93. MR556903
  4. [Ha2] G.A. Hagedorn, Semiclassical quantum mechanics III: the large order asymptotics and more general states. Ann. Phys., t. 135, 1981, p. 58-70. MR630204
  5. [Ha3] G.A. Hagedorn, Semiclassical quantum mechanics IV: large order asymptotics and more general states in more than one dimension. Ann. Inst. Henri Poincaré, t. 42, n° 4, 1985, p. 363-374. Zbl0900.81053MR801234
  6. [Hu] W. Hunziker, The S-matrix in classical mechanics. Commun. Math. Phys., t. 8, 1968, p. 282-299. Zbl0159.55001
  7. [LS] L. Loomis and S. Sternberg, Advanced Calculus. Reading, Mass., Adison-Wesley, 1968. Zbl0162.35301MR227327
  8. [R] S. Robinson, The semiclassical limit of quantum dynamics I: time evolution. J. Math. Phys., t. 29, n° 2, 1988, p. 412-419. Zbl0647.46060MR927028
  9. [RS1] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. II, Fourier Analysis, Self-Adjointness. Academic Press, New York, London, 1975. Zbl0308.47002
  10. [RS2] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. III, Scattering Theory. Academic Press, New York, London, 1979. Zbl0405.47007MR529429
  11. [Sie] C.L. Siegel, Vorlesungen über Himmelsmechanik. Springer Verlag, Berlin, Göttingen, Heidelberg, 1956. Zbl0070.45403MR80009
  12. [Sim] B. Simon, Wave operators for classical particle scattering. Commun. Math. Phys., t. 23, 1971, p. 37-48. Zbl0238.70012MR294899
  13. [SY] A.V. Sobolev and D.R. Yafaev, On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics. Preprint, Leningrad, 1985. 
  14. [Y1] K. Yajima, The quasi-classical limit of quantum scattering theory. Commun. Math. Phys., t. 69, 1979, p. 101-129. Zbl0425.35076
  15. [Y2] K. Yajima, The quasi-classical limit of quantum scattering theory II. Long-range scattering. Duke Math. J., t. 48, n° 1, 1981, p. 1-22. Zbl0454.35069
  16. [Y3] K. Yajima, The quasi-classical limit of scattering amplitude I. Finite range potentials. Preprint, Tokyo, 1984. 

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