High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials

George A. Hagedorn

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

  • Volume: 47, Issue: 1, page 1-16
  • ISSN: 0246-0211

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Hagedorn, George A.. "High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials." Annales de l'I.H.P. Physique théorique 47.1 (1987): 1-16. <http://eudml.org/doc/76369>.

@article{Hagedorn1987,
author = {Hagedorn, George A.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {quantum mechanical systems; eigenvalues; eigenvectors; Hamiltonian; Born- Oppenheimer approximation},
language = {eng},
number = {1},
pages = {1-16},
publisher = {Gauthier-Villars},
title = {High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials},
url = {http://eudml.org/doc/76369},
volume = {47},
year = {1987},
}

TY - JOUR
AU - Hagedorn, George A.
TI - High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials
JO - Annales de l'I.H.P. Physique théorique
PY - 1987
PB - Gauthier-Villars
VL - 47
IS - 1
SP - 1
EP - 16
LA - eng
KW - quantum mechanical systems; eigenvalues; eigenvectors; Hamiltonian; Born- Oppenheimer approximation
UR - http://eudml.org/doc/76369
ER -

References

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  1. [1] M. Born, R. Oppenheimer, Zur Quantentheorie der Molekeln. Ann. Phys. (Leipzig), t. 84, 1927, p. 457-484. Zbl53.0845.04JFM53.0845.04
  2. [2] J.M. Combes, On the Born-Oppenheimer Approximation. In: International Symposium on Mathematical Problems in Theoretical Physics (ed. H. Araki), p. 467-471. Berlin, Heidelberg, New York, Springer, 1975. MR673617
  3. [3] J.-M. Combes, The Born-Oppenheimer Approximation. In: The Schrödinger Equation (eds. W. Thirring, P. Urban), p. 139-159. Wien, New York, Springer, 1977. Zbl0372.47026MR673617
  4. [4] J.-M. Combes, P. Duclos and R. Seiler, The Born-Oppenheimer Approximation. In: Rigorous Atomic and Molecular Physics (eds. G. Velo, A. Wightman), p. 185-212. New York, Plenum, 1981. 
  5. [5] G.A. Hagedorn, A Time Dependent Born-Oppenheimer Approximation. Commun. Math. Phys., t. 77, 1980, p. 1-19. Zbl0448.70013MR588684
  6. [6] G.A. Hagedorn, Higher Order Corrections to the Time-Dependent Born-Oppenheimer Approximation I: Smooth Potentials. Ann. Math., t. 124, 1986, p. 571-590. Erratum to appear 1987. Zbl0619.35094MR866709
  7. [7] G.A. Hagedorn, Multiple Scales and the Time-Independent Born-Oppenheimer Approximation (submitted to the proceedings of The International Conference on Differential Equations and Mathematical Physics, Birmingham, Alabama. March, 1986). 
  8. [8] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. IV, Analysis of Operators, New York, London, Academic Press, 1978. Zbl0401.47001
  9. [9] R. Seiler, Does the Born-Oppenheimer Approximation Work ?Helv. Phys. Acta, t. 46, 1973, p. 230-234. 
  10. [10] B. Simon, Semiclassical Analysis of Low Lying Eigenvalues. I. Non-degenerate Minima: Asymptotic Expansions. Ann. Inst. Henri Poincaré Sect A, t. 38, 1983, p. 295-308. Zbl0526.35027MR708966

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