WKB validity condition ($|\hslash p^{\prime }/p^2|\ll 1$)

For $p(x)=\sqrt{2m[E-V(x)]}$ in a classically allowed region, a local validity condition is $|\hslash p^{\prime }/p^2|\ll 1$. The momentum changes little during a local oscillation. It fails at an ordinary turning point where $p=0$, requiring an Airy turning-point connection formula.