Q#2 (a) The relation for total energy (E) and momentum (p) for a relativistic particle is E = c² p² + m²c*, wherem is the rest mass and c is the velocity of light. Using the relativistic relations E = h w and p = hk, where w isthe angular frequency and k is the wave number, show that the product of group velocity and the phase velocityis equal to c2.

Since, vp=ωk....(1)where, ω is angular velocityand k is propagation vectorvp=ωk=hωhk=Ep.....…

Q#2 (a) The relation for total energy (E) and momentum (p) for a relativistic particle is E = c²p² + m²c*, where m is the rest mass and c is the velocity of light. Using the relativistic relations E= ho and p= ħk, where o is the angular frequency and k is the wave number, show that the product of group velocity and the phase velocity is equal to c?.

Q#2 (a) The relation for total energy (E) and momentum (p) for a relativistic particle is E = c²p² + m²c*, where m is the rest mass and c is the velocity of light. Using the relativistic relations E= ho and p= ħk, where o is the angular frequency and k is the wave number, show that the product of group velocity and the phase velocity is equal to c?.