Wavenumber - in Wave Equations

In Wave Equations

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 v_p is the phase velocity of the wave.

For the special case of an electromagnetic wave in vacuum, where v_p = 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.