what is the relation between particle velocity and wave velocity?
Particle velocity is related to the group velocity of wave, V_g=d(omega)/d(k), k=2*pi/lambda, not to its phase velocity V_ph=omega/k. For a free particle, kinetic energy E=p^2/(2*m), thus dispersion of the De Broglie's wave is omega=(h_bar*k^2)/(2*m).