Let $0<\hbar\le \hbar_0$ be the semiclassical parameter, and consider the stationary Schrödinger equation
\begin{align*}
-\frac{\hbar^2}{2m}\psi''+V\psi=E\psi.
\end{align*}
Suppose $V$ is $C^2$ near a simple turning point $x_0$, with $V(x_0)=E$ and $V'(x_0)>0$, and consider points separated from the Airy transition scale by $|x-x_0|\gg \hbar^{2/3}$. Define
\begin{align*}
p(x)=\sqrt{2m(E-V(x))}\quad \text{for }x<x_0.
\end{align*}
On the forbidden side define
\begin{align*}
q(x)=\sqrt{2m(V(x)-E)}\quad \text{for }x>x_0.
\end{align*}
Away from $x_0$, the decaying WKB solution on the forbidden side $x>x_0$,
\begin{align*}
\psi(x)\sim \frac{C}{\sqrt{q(x)}}\exp\left(-\frac{1}{\hbar}\int_{x_0}^{x}q(s)\,ds\right),
\end{align*}
continues to the oscillatory-side expression
\begin{align*}
\psi(x)\sim \frac{2C}{\sqrt{p(x)}}\sin\left(\frac{1}{\hbar}\int_x^{x_0}p(s)\,ds+\frac{\pi}{4}\right)
\end{align*}
for $x<x_0$, with leading asymptotic accuracy as $\hbar\to0$ in the region $|x-x_0|\gg \hbar^{2/3}$. If $V'(x_0)<0$, the same formula applies after reversing left and right.