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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 is minimal for Z = 27/16 implying shielding reduces the effective charge to ~1.69. Substituting this value of Z into the expression for H yields 729E 1 /128 = −77.5 eV, within 2% of the experimental value, −78.975 eV. [5] Even closer estimations of this energy have been found using more complicated trial wave functions with more ...
In magnetohydrodynamics (MHD), shocks and discontinuities are transition layers where properties of a plasma change from one equilibrium state to another. The relation between the plasma properties on both sides of a shock or a discontinuity can be obtained from the conservative form of the MHD equations, assuming conservation of mass, momentum, energy and of .
In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid , incompressible and irrotational .
The R wave and the L wave are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ω R (hence the designation of this frequency) and a resonance at ω c. The L wave has a cut-off at ω L and no resonance. R waves at frequencies below ω c /2 are also known as whistler modes. [6]
Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the ...
Quantum reflection is a classically counterintuitive phenomenon whereby the motion of particles is reverted "against the force" acting on them. This effect manifests the wave nature of particles and influences collisions of ultracold atoms and interaction of atoms with solid surfaces.
A sound wave propagates through a material as a localized pressure change. Increasing the pressure of a gas or fluid increases its local temperature. The local speed of sound in a compressible material increases with temperature; as a result, the wave travels faster during the high pressure phase of the oscillation than during the lower pressure phase.