Hbar Conventions

The default convention keeps $\hbar$ explicit. Pages may set $\hbar=1$ only after declaring it.

Where Hbar Appears

Structure	Explicit Convention
Commutator	$[x,p]=i\hbar$
Momentum operator	$p=-i\hbar\,d/dx$
Time evolution	$U(t)=\exp(-iHt/\hbar)$
de Broglie relation	$p=\hbar k$
Energy-frequency relation	$E=\hbar\omega$
Spin eigenvalues	$J_z\lvert j,m\rangle=\hbar m\lvert j,m\rangle$

Hbar Equals One Translation

$\hbar=1$ Formula	Explicit Formula
$[x,p]=i$	$[x,p]=i\hbar$
$p=-i\,d/dx$	$p=-i\hbar\,d/dx$
$e^{-iEt}$	$e^{-iEt/\hbar}$
$p=k$	$p=\hbar k$
$J_z\lvert j,m\rangle=m\lvert j,m\rangle$	$J_z\lvert j,m\rangle=\hbar m\lvert j,m\rangle$

Common Mistakes

• Setting $\hbar=1$ in a phase but not in commutators.
• Forgetting that $j$ and $m$ are dimensionless labels.
• Comparing numerical frequencies with energies after setting $\hbar=1$.
• Treating $h$ and $\hbar$ as interchangeable; $h=2\pi\hbar$.

Canonical Links

• Units and Constants
• Natural Units
• Angular Momentum Convention Translator
• Fourier Convention Translator

References

• R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.