Divergence-free WKB theory (Q1827542)

Semiclassical theories in quantum dynamics are important, though they are neither classical nor quantum, because they develop new mathematical methods and give useful intuitive insights. The modified WKB theory developed in this paper is based on an approximate reduction of the Schrödinger equation to a cubic algebraic equation in momentum space by including the nonperturbative quantum correction to the usual quadratic approximation. The zeroth-order solution, which is given by a root of the cubic equation includes quantum correction to the bare classical limit \(ip(x;E)\) and is interpreted as a \textit{dressed momentum}. Various ramifications and applications are worked out and discussed.