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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Remarks on the Born-Oppenheimer approximation

José Wudka

Published Jan 15, 1990• 6 citations
Publisher

Abstract

The Born-Oppenheimer formulas, as modified by the introduction of the adiabatic connection, are derived from the effective action obtained by integrating out the fast variables. The parallels and differences with Berry's approach are stressed, and the corrections to the approximation are investigated.
DOI
10.1103/physrevd.41.712

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We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the rst time when a band crossing is encountered. The adiabatic decoupling leads to an eective Schrodinger equation for the nuclei, including contributions from the Berry connection. 1
By extending the Born-Oppenheimer approximation improved by Wilczek et al. to deal with separation of the spin and space coordinates of a particle in an external field, we generally discuss the direct effects of an induced gauge field and the higher-order corrections to the problem. It is shown that Bitter and Dubbers's experiment about Berry's phase is directly explained as an effect of the induced gauge potential in terms of the first-order approximation in this paper. The higher-order effects appearing in this experiment are also pointed out when the adiabatic conditions are broken.