Planck’s constant, *h*, appears throughout quantum mechanics and is one of the fundamental constants of physics. It has a value of:

*h = 6.6260693(11) x 10 ^{-34} J s*

where uncertain values in the decimal place are contained in brackets. Planck’s constant has the units of action ( *energy* x *time*, which can be shown to be the same as *momentum* x *length* ).

Planck’s constant was first identified as part of Max Planck’s description of blackbody radiation. Later, it was shown by Albert Einstein to be the constant of proportionality between the energy ( *E* ) and frequency ( *f* ) of photons:

*E = hf*

A closely-related quantity (usually pronounced “h-bar”) is:

*ħ = h/2π = 1.054571596(82) x 10 ^{-34}J s*

In this form, Planck’s (reduced) constant appears in the two uncertainty relationships:

ΔxΔp ≥ ħ |
and | ΔEΔt ≥ ħ |

where we have uncertainties in the measurements of a particle’s

or wave-packet’s position *Δx*, momentum *Δp*, energy *ΔE* and lifetime *Δt*.

In Planck units, or natural units, *ħ = 1, c = 1*.

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