TITLE:
The Born-Oppenheimer Approximation Revisited
AUTHORS:
Hubert Klar
KEYWORDS:
Born-Oppenheimer, Adiabaticity, Wannier Phenomenon
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.8,
August
14,
2020
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.