JAMP  Vol.8 No.8 , August 2020
The Born-Oppenheimer Approximation Revisited
Abstract: We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.
Cite this paper: Klar, H. (2020) The Born-Oppenheimer Approximation Revisited. Journal of Applied Mathematics and Physics, 8, 1507-1514. doi: 10.4236/jamp.2020.88116.

[1]   Born, M. and Oppenheimer, R. (1927) Zur Quantentheorie der Molekeln. Annalen der Physik, 389, 457-484.

[2]   Macek, J.H. (1968) Properties of Autoionizing States of He. Journal of Physics B: Atomic and Molecular Physics, 1, 831.

[3]   Klar, M. and Klar, H. (1980) An Accurate Treatment of Two-Electron Atoms using Hyperspherical Coordinates. Journal of Physics B: Atomic and Molecular Physics, 13, 1057.

[4]   Wannier, G. (1953) The Threshold Law for Single Ionization of Atoms or Ions by Electrons. Physical Review, 90, 817.

[5]   Sommerfeld, A. (1944) Atombau und Spektrallinien. Springer. Berlin.

[6]   See Any Textbook on Functional Analysis.

[7]   Fano, U. (1961) Effects of Configuration Interaction on Intensities and Phaseshifts. Physical Review, 124, 1866.

[8]   Klar, H. (2018) Electron Wave Propagation near a Potential Ridge. Physical Review Letters, 120, Article ID: 053401.