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In condensed matter physics and atomic physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes. When an atom decays from an excited electronic state at rest to a lower energy electronic state by the spontaneous emission of a photon, due to conservation of momentum, the atom gains momentum equivalent to the momentum of the photon.
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: =.
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change ...
The photon having non-zero linear momentum, one could imagine that it has a non-vanishing rest mass m 0, which is its mass at zero speed. However, we will now show that this is not the case: m 0 = 0. Since the photon propagates with the speed of light, special relativity is called for. The relativistic expressions for energy and momentum ...
where is the energy, is the momentum, and is the rest mass, when the rest mass tends to be zero, e.g. for a photon, or the momentum tends to be large, e.g. for a large-speed proton, this relation will collapses into a linear dispersion, i.e.
The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.
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.