When was the reduced planck constant $\hbar= h/2\pi$ first introduced and what was the reason behind introducing such a constant?

I know that $E=\hbar \omega$ and $p=\hbar k$ and writing again and again the $2\pi$ in $E=(h/2\pi)\omega$ $p=(h/2\pi) k$ etc. must really annoy the physicist of the time. However there are alternatives to these quantities namely $E=h \nu$ and $p=h/\lambda$. What was the reason preferring $\omega$ and $k$ over $\nu$ and $\lambda$ at the cost of introducing a new constant


1 Answer 1


As none of the answer on physics give the historical significance of the introduction, I'll give it a try.

Bohr first introduced $\hbar$ as the quantum of angular momentum (when $h$ is the quantum of action). Bohr believed it to be the angular momentum of each electron in an atom. Despite this being false, both Heisengberg and Schrödinger parallel work on quantization rules for electron (circa 1925) kept the reduced Plank constant as the fundamental quantum of angular momentum. For this reason, Heisenberg was familiar with $\hbar$, and he stated his 1927 uncertainty principle in terms of $\hbar$ rather than $h$, ensuring a bright future to the constant, that is sometime named Dirac constant because Dirac was the first one to use the notation (Bohr referred to it as $M_0$).

Note that some physicist believe it to be the angular derivative of the (not reduced) Planck constant.

  • $\begingroup$ I don't think Bohr was the one who used $\hbar$. It is true that he postulated that the angular momentum should be an integer multiple of $h/2\pi$ but I doubt that he used $\hbar$. $\endgroup$
    – Gonenc
    May 8, 2015 at 20:39
  • $\begingroup$ In "On the Constitution of Atoms and Molecules" he uses $M_0$. I wasn't talking about the symbol $\hbar$, which was given by Dirac (hence the name "Dirac constant") $\endgroup$
    – VicAche
    May 8, 2015 at 21:18

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