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The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
Essential for water waves, and other wave phenomena in physics, is that free propagating waves of non-zero amplitude only exist when the angular frequency ω and wavenumber k (or equivalently the wavelength λ and period T) satisfy a functional relationship: the frequency dispersion relation [4] [5]
Dispersion. Light waves of all frequencies travel at the same speed of light while matter wave velocity varies strongly with frequency. The relationship between frequency (proportional to energy) and wavenumber or velocity (proportional to momentum) is called a dispersion relation.
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity , and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity .
A nonlinear dispersion relation (NDR) is a dispersion relation that assigns the correct phase velocity to a nonlinear wave structure. As an example of how diverse and intricate the underlying description can be, we deal with plane electrostatic wave structures ϕ ( x − v 0 t ) {\displaystyle \phi (x-v_{0}t)} which propagate with v 0 ...
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. [1] Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance.