csoportsebesség

Csoportsebesség refers to the speed at which the overall shape or envelope of a wave packet travels. A wave packet is a localized wave that is a superposition of waves with slightly different frequencies and wavelengths. While individual sinusoidal components of the wave packet travel at their own phase velocity, the group velocity describes the propagation of the energy and information carried by the wave packet.

In a dispersive medium, where the phase velocity depends on frequency, the group velocity can be different from the phase velocity. If the group velocity is less than the phase velocity, the medium is said to be normally dispersive. If the group velocity is greater than the phase velocity, the medium is said to be anomalously dispersive. In a non-dispersive medium, the group velocity and phase velocity are equal.

The group velocity (vg) can be mathematically expressed as the derivative of the angular frequency (ω) with respect to the wave number (k): vg = dω/dk. This relationship is fundamental in describing wave propagation in various physical systems, including optics, quantum mechanics, and water waves. For instance, in quantum mechanics, the group velocity of a matter wave packet corresponds to the classical velocity of the particle. Understanding group velocity is crucial for analyzing phenomena such as wave packet spreading and signal transmission.