1. A wave packet, also called wave group, can be described in terms of a superposition of plane waves of different wavelengths. The phase velocity, i.e., the rate at which the wave propagates, is given by vp =w/k where w and k denote the angular frequency and wave number, respectively. The wave group has a velocity different from the phase velocities of the waves that make it up, which is called the group velocity given by vg = dw/dk. For the de Broglie wave of a particle with relativistic momentum p = ymv and relativistic energy E = ymc²: a) Calculate vp and vg. b) Show that (i) the de Broglie group velocity is the speed of the particle and (ii) the de Broglie phase velocity is greater than c.

1. A wave packet, also called wave group, can be described in terms of a superposition of plane waves of different wavelengths. The phase velocity, i.e., the rate at which the wave propagates, is given by vp =w/k where w and k denote the angular frequency and wave number, respectively. The wave group has a velocity different from the phase velocities of the waves that make it up, which is called the group velocity given by vg = dw/dk. For the de Broglie wave of a particle with relativistic momentum p = ymv and relativistic energy E = ymc²: a) Calculate vp and vg. b) Show that (i) the de Broglie group velocity is the speed of the particle and (ii) the de Broglie phase velocity is greater than c.