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Born-Oppenheimer wave function near level crossing J. E. Avron and A. Gordon

Summary: Born-Oppenheimer wave function near level crossing
J. E. Avron and A. Gordon
Department of Physics, Technion, 32000 Haifa, Israel
Received 18 June 2000; published 3 November 2000
The standard Born-Oppenheimer theory does not give an accurate description of the wave function near
points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the
crossing energy. This leads to the study of two coupled second-order ordinary differential equations whose
solution is described in terms of the generalized hypergeometric functions of the kind 0F3(;a,b,c;z). We find
that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like 1/6
, where is the
electron to nuclear mass ratio.
PACS number s : 31.15.Gy, 33.55.Be, 33.20. t
In 1927, in a landmark paper, Born and Oppenheimer 1
paved the way toward applying quantum mechanics to mo-
lecular spectra. In their paper they introduced an approxima-
tion that greatly simplified the treatment of quantum-
mechanical spectral problems in which the particles can be
divided into heavy and light. Molecules are an example since
the nuclei are much heavier than the electrons. We shall


Source: Avron, Joseph - Physics Department, Technion, Israel Institute of Technology


Collections: Physics