Relationship between Group Velocity and Particle Velocity

[jsmith1994]

Homework Statement

Prove that the group velocity of a wave packet is equal to the particle’s velocity
for a relativistic free particle.

Homework Equations

v_group = Δω/Δk = dω/dk
E = (h/2π)*ω = √(p²c² + m²c⁴)

The Attempt at a Solution

I'll be honest..I have no idea where to even begin with this problem.

I know that v_particle = f*λ but I've got no idea how to begin besides that. If anyone could help with that it'd be great.

Thanks!

 

[Goddar]

You must have seen what the wave packet solution is for a free particle, so start with that and see what ω is there and relate this to your first equation Δω/Δk.
Do you obtain something familiar? (hint: in terms of momentum?)