SI Units

SI units are the default whenever numerical laboratory scales, dimensions, or electromagnetic units matter.

Default Convention

Keep constants explicit:

$$E=\hbar\omega, \qquad p=\hbar k, \qquad [x,p]=i\hbar.$$

For electromagnetic coupling in SI,

$$H=\frac{1}{2m}(\mathbf p-q\mathbf A)^2+q\Phi.$$

Exact Defining Constants

The defining constants most often used in quantum mechanics are $c$, $h$, $e$, $k_B$, and $N_A$. Use Constants for numerical values and source policy.

Dimensional Anchors

Quantity	SI Dimension
$\hbar$	action, $\mathrm{J\,s}$
$c$	speed, $\mathrm{m\,s^{-1}}$
$e$	charge, $\mathrm C$
$k_B T$	energy, $\mathrm J$
$\epsilon_0$	SI electric-field convention
$\mu_0$	SI magnetic-field convention

Common Mistakes

• Dropping $4\pi\epsilon_0$ from Coulomb potentials while still calling the formula SI.
• Using $e$ as the electron charge instead of the positive charge magnitude.
• Treating $\omega$ and $\nu$ as interchangeable: $E=\hbar\omega=h\nu$.
• Assuming $\mu_0=4\pi\times10^{-7}\ \mathrm{N\,A^{-2}}$ is exact after the SI redefinition.

Canonical Links

• Units and Constants
• Constants
• Units
• Charge Sign Conventions

References

• BIPM SI Brochure
• NIST CODATA Fundamental Physical Constants