Note on Group Velocity and Energy Propagation

A general proof is given for the equality between group velocity and energy velocity for linear wave propagation in a homogeneous medium with arbitrary spatial and temporal dispersion. In the series of physics “Questions” in the American Journal of Physics, K. M. Awati and T. Howes ask for a general proof of the fact that in linear dispersive wave propagation, energy propagates at the group velocity [1]. Several answers to this question have appeared recently [2], but a general proof has not been provided by any of them. For a stable and nondissipative [3] medium, such a general proof is indeed available from classical, continuum electrodynamics of media [4]. It can be readily argued that this type of proof