Wavenumber - in Wave Equations

In Wave Equations

See also: Wavenumber–frequency diagram

In general, the angular wavenumber k, the magnitude of the wave vector, is given by

where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and vp is the phase velocity of the wave.

For the special case of an electromagnetic wave in vacuum, where vp = c, k is given by

where E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in a vacuum.

For the special case of a matter wave, for example an electron wave, in the non-relativistic approximation:

Here p is the momentum of the particle, m is the mass of the particle, E is the kinetic energy of the particle, and ħ is the reduced Planck's constant.

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