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 (
N·
m·
s), which are the units of
angular momentum.
A closely-related quantity is the
reduced Planck constant (sometimes called
Dirac's constant):
-
where π is the constant
pi. This constant is pronounced as "h-bar".
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
-
There are a number of other such pairs of physically measurable values which obey a similar rule.
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
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