dispersionsrelation
A dispersion relation, also known as a dispersion law, is a functional relationship between frequency ω (or f) and wavenumber k (or wavevector) for waves in a given medium or system. It describes how waves of different wavelengths propagate and determines the phase velocity v_p = ω/k and the group velocity v_g = dω/dk, which govern the motion of individual wave crests and of wave packets, respectively.
In continuous media, the dispersion relation expresses how ω depends on k for that medium. Examples include
In solids and lattices, dispersion relations relate energy and momentum. Phonons have ω(k) determined by interatomic
Dispersion relations explain phenomena such as the spreading of wave packets, frequency-dependent refraction, and the existence