h

The symbol $h$ denotes the Planck constant. The reduced Planck constant is

$$\hbar=\frac{h}{2\pi}, \qquad h=2\pi\hbar.$$

Default Meaning

This site usually writes formulas using $\hbar$ rather than $h$ when angular frequency, commutators, or Schrödinger evolution are involved. The symbol $h$ appears naturally with ordinary frequency $\nu$:

$$E=h\nu.$$

For angular frequency $\omega=2\pi\nu$,

$$E=\hbar\omega.$$

Units

$h$ has units of action, equivalently energy times time or angular momentum.

Common Collisions

• $h$ as a numerical step size in finite-difference or numerical methods.
• $h$ as height or a generic small perturbation.
• $h_{\mu\nu}$ as a metric perturbation in field-theory contexts.

Canonical Links

• Units and Constants
• hbar
• Quantum Harmonic Oscillator

References

• D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
• R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.