The Born-Oppenheimer Approximation

  • J.-M. Combes
Part of the Acta Physica Austriaca book series (FEWBODY, volume 17/1977)


The paper I want talk about [1] was written in 1927, one year after the Schrodinger equation, and I am sure than next year some people in molecular physics will celebrate the fiftieth anniversary of one of the most famous out come of this equation which has been during those fifty years the basis of the phenomenological interpretation of molecular spectra. Another virtue of their work is of mathematical nature since the problem they had to deal with, as we will see later, lies definitely in the field of singular perturbation theory, almost undeveloped mathematically the problem is singular because for molecular systems one has a very small mass ratio (~ 10-3) between the electronic and nuclear components. So one is templed to make some kind of classical approximation for the low speed (high mass) one.


Canonical Transformation Schrodinger Equation Singular Perturbation Theory Electronic Term Mathematical Nature 
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  1. 1.
    M. Born, R. Oppenheimer, Ann. Phys. 84, 475, 1927.Google Scholar
  2. 2.
    P. Aventini, R. Seiler, Commun. math. Phys. 41, 119, 1975.MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    J. M. Combes, A. Grossmann, R. Seiler, To appear.Google Scholar
  4. 4.
    T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York 1966.MATHGoogle Scholar
  5. 5.
    J. M. Combes, Proceedings of the Conference on Spectral and Scattering Theory, RIMS Kyoto, Janvier 1975.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • J.-M. Combes
    • 1
    • 2
    • 3
  1. 1.Centre de Physique ThéoriqueMarseille Cedex 2France
  2. 2.Depart. de Mathém.Centre Universitaire de ToulonFrance
  3. 3.Centre de Physique ThéoriqueCNRS MarseilleFrance

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