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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 ...
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
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.
To calculate the density of states we rewrite equation as follows: = , where n is the norm of the vector n = (n 1, n 2, n 3). For every vector n with integer components larger than or equal to zero, there are two photon states.
For photons, this is the relation, discovered in 19th century classical electromagnetism, between radiant momentum (causing radiation pressure) and radiant energy. If the body's speed v is much less than c , then ( 1 ) reduces to E = 1 / 2 m 0 v 2 + m 0 c 2 ; that is, the body's total energy is simply its classical kinetic energy ...
A spectroscopic wavenumber can be converted into energy per photon E by Planck's relation: = ~. It can also be converted into wavelength of light: = ~, where n is the refractive index of the medium. Note that the wavelength of light changes as it passes through different media, however, the spectroscopic wavenumber (i.e., frequency) remains ...
Maxwell–Boltzmann statistics is used to derive the Maxwell–Boltzmann distribution of an ideal gas. However, it can also be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (resulting in Maxwell–Jüttner distribution), and to other than three-dimensional spaces.