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These equations say respectively: a photon has zero rest mass; the photon energy is hν = hc|k| (k is the wave vector, c is speed of light); its electromagnetic momentum is ħk [ħ = h/(2π)]; the polarization μ = ±1 is the eigenvalue of the z-component of the photon spin.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
In 1900 Max Planck, attempting to explain black-body radiation, suggested that although light was a wave, these waves could gain or lose energy only in finite amounts related to their frequency. Planck called these "lumps" of light energy "quanta" (from a Latin word for "how much").
The equation PV = nRT represents the ideal gas law, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. Gibbs's free energy formula
Both differential equations have the form of the general wave equation for waves propagating with speed , where is a function of time and location, which gives the amplitude of the wave at some time at a certain location: = This is also written as: = where denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as
Maxwell's equations in curved spacetime, commonly used in high-energy and gravitational physics, are compatible with general relativity. [ note 2 ] In fact, Albert Einstein developed special and general relativity to accommodate the invariant speed of light, a consequence of Maxwell's equations, with the principle that only relative movement ...
Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile". Each propagates at generally different speeds determined by the important function called the dispersion relation .
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: =.