Double-well potential: The WKB approximation with phase loss and anharmonicity effect

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and the 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 the anharmonicity effect considered leads to a great improvement in the accuracy of the WKB approximation.