WKB approximation

Summary

The WKB approximation gives approximate solutions of linear differential equations whose highest derivative is multiplied by a small parameter, such as $\varepsilon^2 y'' = Q(x) y$. It writes the solution as the exponential of a series in $\varepsilon$ and keeps the first terms. It is also called the Liouville–Green method, and the name WKB refers to Wentzel, Kramers and Brillouin. It is the basis of semiclassical approximations in quantum mechanics and of the asymptotics of special functions.