Q1andQ2

[20%] A plasmon has a dispersion relation w(k) = wil + c2k2, which relates the angular frequency w and the wave number k. Wp and c are constants. (a) [7%] What is the phase velocity as a function of W, vp(W)? (b) [7%] What is the group velocity as a function of w, v,(W)? (c) [6%] In what frequency range there is no propagating wave? [20%] A photon of initial wave length 2 experiences a Compton 180°-backward scattering by a rest electron, and then the photon's wave length changes to 2'. Let the rest mass of the electron be mand the speed of light be c. (a) [6%) What is the momentum of the electron after the scattering (in terms of 1 and 2')? (b) [7%] Show the equation expressing conservation of energy. (c) [7% Solve the relation between 1 and from above conditions.