Hybrid Taylor-WKB series

A generalized WKB approach for constructing WKB series endowed with some properties of Taylor ones is presented. Apart from the Riccati equation itself its formalism involves also the Riccati-equation’s derivatives (REDs) obtained by differentiating of the former with respect to a spatial variable. For any smooth potential barrier given in the finite spatial interval to include turning points, the zeroth-order term of presented WKB series is regular everywhere in this interval. Moreover, the more REDs are used, the more exact the zeroth-order solution is.