Planck's constant
Planck's constant, denoted h, is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory. It has a value of approximately
Planck's constant has
units of
energy multiplied by
time, which are the units of
action. These units may also be written as
momentum times
distance (
Nms), which are the units of
angular momentum.
A closely-related quantity is
where π is the constant
pi. This constant, which is pronounced as "h-bar", is sometimes (though infrequently) referred to as
Dirac's constant, after
Paul Dirac.
Planck's constant is used to describe quantization, a phenomenon occurring in microscopic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values. For instance, the energy E carried by a beam of light with constant frequency ν can only take on the values
It is sometimes more convenient to use the
angular frequency ω=2πν, which gives
Many such "quantization conditions" exist. A particularly interesting condition governs the quantization of
angular momentum. Let
J be the total angular momentum of a system with rotational invariance, and
Jz the angular momentum measured along any given direction. These quantities can only take on the values
Thus, may be said to be the "quantum of angular momentum".
Planck's constant also occurs in statements of Heisenberg's uncertainty principle. The uncertainty in any position measurement, Δx, and the uncertainty in a momentum measurement along the same direction, Δp, obeys
On some browsers, the
unicode symbol ℎ (ℎ) is rendered as Planck's constant, and the symbol ℏ (ℏ) is rendered as Dirac's constant.
See also