Uniform semiclassical theory of avoided crossings

Abstract

A voided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of avoided crossings is presented in this article for the case where that behavior is generated by a classical resonance. A low order perturbation theory expression is used as the basis for a functional form for the treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals) obtained from classical trajectory data. The results are compared with quantum mechanical results for the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are described.

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