Quantum rate theory for a symmetric double-well potential

Abstract

A quantum rate theory is presented for a symmetric double‐well potential which is defined by a piecewise quadratic function. The theory is based on stationary states which are decomposed into‐ and left‐moving states. The flux and transmission coefficients for the latter are found in terms of parabolic cylinder functions and are thermally averaged. Close analogies between the quantum and classical formulations are found when an appropriate phase space representation is used. The theory shows good agreement with experimental results for the diffusion of hydrogen and deuterium in niobium, but the agreement is poorer for the same process with the host metal vanadium and the theory does not predict the observed anomalous isotope effect for this process in palladium.