In the [semiclassical WKB approximation](https://en.wikipedia.org/wiki/WKB_approximation) the [Planck constant](https://en.wikipedia.org/wiki/Planck_constant) $\hbar$ is _not_ a fixed number equal to its physical value $\approx 1.05 \times 10^{-34} Js$. Instead it is an [indeterminate](https://en.wikipedia.org/wiki/Indeterminate_(variable)). The semiclassical WKB expansion is an [asymptotic expansion](https://en.wikipedia.org/wiki/Asymptotic_expansion) in the limit $\hbar\to 0^+$.