Dirac constant

Characters with a similar style: ħ · · · ·

The constant Dirac , or Planck – Dirac constant , is the rarely used name for the reduced Planck constant $\hbar \equiv h/2\pi$ ${\ displaystyle \ hbar \ equiv h / 2 \ pi}$ $\ hbar \ equiv h / 2 \ pi$ - coefficient connecting angular frequency $\omega =2\pi \nu$ ${\ displaystyle \ omega = 2 \ pi \ nu}$ ${\ displaystyle \ omega = 2 \ pi \ nu}$ ( $\nu$ ${\ displaystyle \ nu}$ $\ nu$ - frequency ) of a photon (or another quantum) with its energy: $E=h\nu =\hbar \omega .$ ${\ displaystyle E = h \ nu = \ hbar \ omega.}$ ${\ displaystyle E = h \ nu = \ hbar \ omega.}$ Here $h$ ${\ displaystyle h}$ $h$ - Planck's (unreduced) constant. Dirac usually constant $\hbar$ ${\ displaystyle \ hbar}$ $\ hbar$ referred to as rationalized or reduced Planck constant .

\hbar \equiv {\frac {h}{2\pi }}=1{,}054\ 571\ 800(13)\times 10^{-34}

{\ displaystyle \ hbar \ equiv {\ frac {h} {2 \ pi}} = 1 {,} 054 \ 571 \ 800 (13) \ times 10 ^ {- 34}}

\ hbar \ equiv {\ frac {h} {2 \ pi}} = 1 {,} 054 \ 571 \ 800 (13) \ times 10 ^ {{- 34}}

J · c =

6{,}582\ 119\ 514(40)\cdot 10^{-16}

{\ displaystyle 6 {,} 582 \ 119 \ 514 (40) \ cdot 10 ^ {- 16}}

{\ displaystyle 6 {,} 582 \ 119 \ 514 (40) \ cdot 10 ^ {- 16}}

eV · s ^[1] .

The meaning of the introduction of the reduced Planck constant and its widespread use is that in theoretically more important formulas, when it is used, the blocking factor or divider 2 π disappears. First of all, it refers to the relationship of action and phase $S=\hbar \varphi$ ${\ displaystyle S = \ hbar \ varphi}$ $S = \ hbar \ varphi$ as well as a wave vector pulse $\mathbf {p} =\hbar \mathbf {k}$ ${\ displaystyle \ mathbf {p} = \ hbar \ mathbf {k}}$ $\ mathbf p = \ hbar \ mathbf k$ and energy with cyclical frequency $E=\hbar \omega$ ${\ displaystyle E = \ hbar \ omega}$ $E = \ hbar \ omega$ (more common than a simple frequency that differs from it by a factor of 2 π $\nu$ ${\ displaystyle \ nu}$ $\ nu$ ). As a result, using this form of the Planck constant in general, most formulas are written a little simpler and more transparent.

In the Planck system of units, the reduced (reduced) Planck constant is chosen as the basic unit. Also in theoretical physics, systems of quantities are used (sometimes they are referred to as systems of units) in which the Planck – Dirac constant is one ( $\hbar =1$ ${\ displaystyle \ hbar = 1}$ $\ hbar = 1$ ), which allows us to further simplify the formulas, due to the fact that energy and cyclic frequency, phase and action, momentum and wave vector become pairwise equivalent and interchangeable quantities.

It is denoted by a cross-crossed Latin letter ħ , in formulas it is called “h with a line” ( English h-bar ). In Unicode, this character takes the position U + 0127; there is also a separate character English. Planck constant over two pi (U + 210F, $\hbar$ ${\ displaystyle \ hbar}$ $\ hbar$ ).

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↑ http://physics.nist.gov/cuu/Constants/Table/allascii.txt Fundamental Physical Constants - Complete Listing

[CODATA_allascii-1] ttp://physics.nist.gov/cuu/Constants/Table/allascii.txt Fundamental Physical Constants - Complete Listing

Dirac constant

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