csoportsebességet

Csoportsebesség refers to the speed at which the overall shape of a wave's amplitude, known as the envelope, propagates through space. This is distinct from phase velocity, which describes the speed of a single point of constant phase on the wave. In many simple, non-dispersive media, the group velocity and phase velocity are the same. However, in dispersive media, where the wave speed depends on frequency, these velocities can differ significantly.

The concept of group velocity is particularly important in the study of wave packets, which are localized disturbances formed by the superposition of waves with slightly different frequencies. The envelope of such a wave packet travels at the group velocity. This is crucial in fields like optics, where light pulses are often described as wave packets. In quantum mechanics, the group velocity of a matter wave is related to the velocity of the particle it describes.

Mathematically, group velocity (v_g) is defined as the derivative of the angular frequency (ω) with respect to the wave number (k): v_g = dω/dk. This relationship highlights how the dispersion relation (the function ω(k)) dictates the group velocity. If the dispersion relation is linear (ω = ck), then v_g = c, and the medium is non-dispersive. If the dispersion relation is non-linear, the group velocity will generally differ from the phase velocity (v_p = ω/k). Understanding the distinction and calculation of group velocity is fundamental for analyzing wave propagation in various physical systems.