Consider the following potential
It was shown how to derive the complex energy (near the ground energy) of a resonance in the left well from the Euclidean path integral by Callan and Coleman, see Coleman's book. However I am very interested to derive this complex energy from the WKB method by solving the static Schroedinger equation such that we can give a check for the result derived from the Euclidean path integral. Though it is claimed by Coleman that he (and Callan) did this check. He did not show explicitly how in his original paper as well as the above book.
Coleman did show how to derive the corrected real energy eigenvalue for the symmetric double-well potential in the above book (Appendix 2). And he said that almost identical method can be used to derive the complex energy. I know the complex energy must be related to the pure outgoing boundary condition. But it is still unclear how to arrive that. I would appreciate it very much if you have any idea.