In physics and electrical engineering, dispersion relations describe the interrelations of wave properties like wavelength, frequency, velocities – including phase velocity and group velocity – and refractive index. Besides geometry- and material-dependent dispersion relations, there are the overarching Kramers–Kronig relations that connect the frequency dependences of propagation and attenuation.
Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media.
In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.
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