Phase integral (source code)

= Phase integral
{title2=$\int k(x)\,dx$}

The accumulated phase along a one-dimensional ray. In an oscillatory <WKB approximation>, the two travelling <waves> have phases $\pm\int k\,dx$. In an evanescent region, the positive local decay rate $\kappa=\sqrt{-k^2}$ replaces $k$, producing exponents $\pm\int\kappa\,dx$.