Reduced Planck constant (ℏ) in LaTeX
\hbar produces ℏ, the reduced Planck constant, equal to the Planck constant h divided by 2 pi, and one of the fundamental constants of quantum mechanics.
LaTeX command
\hbarNot the symbol you meant? Draw it to find the command →
\hbar has its own dedicated glyph, with the horizontal bar crossing through the stem of the h, rather than sitting above it. This is the standard physics notation and is a core symbol in both LaTeX and KaTeX, so it never needs a package or a manual workaround.
It appears throughout quantum mechanics: in the energy-frequency relation E = \hbar \omega, in the canonical commutation relation [\hat{x}, \hat{p}] = i\hbar, and in the time-dependent Schrodinger equation, where it multiplies the time derivative of the wavefunction.
Because \hbar is h divided by 2\pi, some derivations switch between the two constants depending on whether angular frequency (\omega) or ordinary frequency (\nu) is more natural for the calculation; keep track of which one you are using when converting between them.
Examples
$E = \hbar \omega$photon energy in terms of angular frequency
$[\hat{x}, \hat{p}] = i\hbar$the canonical commutation relation
$i\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi$the time-dependent Schrodinger equation
Tips and common mistakes
- Type
\hbardirectly rather than building it from\bar{h}; the dedicated symbol has the crossed-stem glyph physicists expect, while\bar{h}draws a plain overline above an italic h and looks noticeably different. - No package is required,
\hbaris available in core LaTeX and in KaTeX. - Remember
\hbar= h / (2\pi); check which constant a formula expects before substituting numerical values. - A rarer variant,
\hslash, exists with a slightly different shape in some fonts, but\hbaris the far more widely supported and recognised choice.
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Convert your maths to LaTeX →FAQ
What is \hbar in LaTeX?
The command for the reduced Planck constant symbol, ℏ, used throughout quantum mechanics.
Do I need a package for \hbar?
No, it is a standard symbol available in core LaTeX and in KaTeX without any extra package.
What's the difference between \hbar and \bar{h}?
\hbar uses a purpose-built glyph with the bar crossing through the stem of the h, the conventional physics notation. \bar{h} instead draws a generic overline accent above an italic h and looks different.
What is h-bar equal to?
\hbar = h / (2\pi), where h is the ordinary (non-reduced) Planck constant.