Reduced Planck constant ($\hslash =h/(2\pi )$)

The reduced Planck constant is $\hslash =h/(2\pi )$, with the same action units as the Planck constant. Since angular frequency is $\omega =2\pi \nu$, a photon's energy can be written $E=\hslash \omega$ instead of $h\nu$.

The reduced Planck constant occurs naturally in the Schrödinger equation, the canonical commutation relation $[X,P]=i\hslash I$, and the Heisenberg uncertainty principle $\Delta X\Delta P\ge \hslash /2$. Comparing a characteristic action with $\hslash$ helps assess a semiclassical approximation, although a large ratio alone does not guarantee that all quantum interference becomes unobservable.