Planck's constant
Planck's constant, denoted <math>h</math>, is a fundamental constant in physics. The current value of Planck's constant is <math>6.626070040(81) \times 10^{-34}</math> Joule-seconds (numbers in brackets represent uncertainty in the last two decimal places).[1]
History
It was first used by Max Planck around 1900 to explain the radiation curves of black-bodies. He supposed that light could be modelled as a series of particles (now called photons), each with an energy proportional to its frequnecy, <math>\nu</math>. The constant of proportionality was Planck's constant. Mathematically this can be expressed as:
<math>E = h \nu</math>
In 1924, Louis De Broglie proposed Wave-particle duality, the idea that matter (protons and electrons for example) had a wave-like nature.[2] Here too, is Planck's constant:
<math>\lambda = \frac{h}{p} </math>
where
- <math>\lambda</math> is the wavelength of the particle
- <math>p</math> is the momentum of the particle
The Planck constant also occurs in equations fundamental to quantum mechanics, such as the Schrodinger equation.
Reduced Planck's Constant
Planck's constant often occurs in equations with the mathematical constant <math>\pi</math>. As such, a factor of <math>\frac{1}{2 \pi}</math> may be taken into Planck's constant as
<math>\hbar = \frac{h}{2 \pi}</math>
The resulting constant is pronounced "h-bar".