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My quantum mechanics book says that $ħ$ is the Planck's constant. The book uses ħ throughout and not one single use of $h$.

My statistical mechanics book says that $h$ is the Planck's constant and doesn't use $ħ$ at all.

Now I know that one of the constant is the other scaled by $2\pi$. But one of them is the Planck's constant and the other is not. Which one of them is true Planck's constant?

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    $\begingroup$ Did you check Wikipedia? $\endgroup$ – Qmechanic May 22 '17 at 12:49
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    $\begingroup$ So my Quantum Mechanics book is wrong. Apparently $h$ is the true Planck constant. But $\hbar$ is is used everywhere and $h$ is used rarely. $\endgroup$ – Ayatana May 22 '17 at 12:58
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    $\begingroup$ What does "true Planck's constant" mean? $h$ is the proportionality constant between the energy of a photon and its "ordinary" frequency and $\hbar$ is the proportionality constant between the energy of a photon and its angular frequency. Which one of these is "true", and why? $\endgroup$ – ACuriousMind May 22 '17 at 13:11
  • $\begingroup$ Related: physics.stackexchange.com/q/153807/2451 $\endgroup$ – Qmechanic May 29 '17 at 1:08
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In the usual terminology we have \begin{align} h &&&\text{Planck's constant} \\ \hbar &= \frac{h}{2\pi} &&\text{reduced Planck's constant} \end{align}

The significance of $2\pi$ here is the ratio between a full circle and a radian, because the energy of a photon is $$ E = hf = \hbar \omega \;,$$ where $f$ is the cyclic frequency of the light and $\omega = 2 \pi f$ is its angular frequency. Both are common because—by long tradition—the frequency and wavelength of waves are generally measured with respect to a full cycle, but mathematical expressions involving waves may be written down more compactly in terms of angular (radian-based) quantities such as the angular frequency and the wavenumber ($k = 2\pi/\lambda$).

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    $\begingroup$ But it is not uncommon to see, as did the OP, the word "reduced" left off the description of $\hbar$. Reader beware. $\endgroup$ – Rococo May 22 '17 at 17:05
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    $\begingroup$ Well, yes. And I do it myself when there is only one of the symbols involved in the discussion, but I encourage people to be specific where there is the possibility of confusion. $\endgroup$ – dmckee --- ex-moderator kitten May 22 '17 at 18:22
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It is $h$. $\hbar$ is $\frac{h}{2π}$.

Planck constant $h$ reduced constant $\hbar = \frac{h}{2\pi}$

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Have a look at the original: 10.1002/andp.19013090310. Planck uses $h$ has it is about the relation of frequency and energy.

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