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The de Broglie relation, [10] [11] [12] also known as de Broglie's momentum–wavelength relation, [4] generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to λ = h / p .
The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =. Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other elementary particles, neutral atoms and molecules in the years since.
The Planck constant, or Planck's constant, denoted by , [1] is a fundamental physical constant [1] of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.
The energy and momentum of an object measured in two inertial frames in energy–momentum space – the yellow frame measures E and p while the blue frame measures E ′ and p ′. The green arrow is the four-momentum P of an object with length proportional to its rest mass m 0.
For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy , it is often used as a unit of temporal frequency assuming a certain speed of light .
The top electron has twice the momentum, while the bottom electron has half. Note that as the momentum increases, the phase velocity decreases down to c, whereas the group velocity increases up to c, until the wave packet and its phase maxima move together near the speed of light, whereas the wavelength continues to decrease without bound. Both ...
In 1900, Max Planck postulated the proportionality between the frequency of a photon and its energy , =, [11] [12] and in 1916 the corresponding relation between a photon's momentum and wavelength, =, [13] where is the Planck constant.
In physics, the thermal de Broglie wavelength (, sometimes also denoted by ) is a measure of the uncertainty in location of a particle of thermodynamic average momentum in an ideal gas. [1] It is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature.