  We investigate the effect of anharmonicity on the WKB approximation in a
double well potential. By incorporating the anharmonic perturbation into the
WKB energy splitting formula we show that the WKB approximation can be greatly
improved in the region over which the tunneling is appreciable. We also observe
that the usual WKB results can be obtained from our formalism as a limiting
case in which the two potential minima are far apart.
