Question

Prove that group velocity is equal to particle velocity

Answer 1

A material particle in motion is equivalent to a group of waves or wave packet.

The group velocity is simply the derivative of frequency ω with respect to propagation constant, from equation (1.11)

or

where  and  

or

.......(1.12)

If E and V represent the total energy and the potential energy of the particle respectively, we have  

therefore

Using de-Broglie formula we have

Substituting this value of in eq (1.12), group velocity will be given by

i.e., Group velocity = particle velocity

HEYA PLS MARK BRAINLIEST