Double-Well Potential : The WKB Approximation with Phase Loss and Anharmonicity Effect

TL;DR

This paper improves the WKB approximation for double-well potentials by incorporating phase loss and anharmonicity effects, significantly enhancing accuracy in tunneling energy calculations.

Contribution

It introduces a generalized WKB energy splitting formula that accounts for phase loss and anharmonicity, improving predictions for tunneling in double-well potentials.

Findings

Enhanced accuracy of WKB approximation with phase loss and anharmonicity effects.

Significant improvement in tunneling energy estimates for moderate potential separations.

Applicable to a broader range of double-well systems than traditional methods.

Abstract

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method gives better results only for large separation between two potential minima. In the range of substantial tunneling, however, the phase loss approach with anharmonicity effect considered leads to a great improvement on the accuracy of the WKB approximation.