The matter-wave dispersion relation given in equation (6-23) is correct only at low speed...

The matter-wave dispersion relation given in equation (6-23) is correct only at low speed and when mass/internal energy is ignored.

(a) Using the relativistically correct relationship among energy, momentum, and mass, show that the correct dispersion relation is

(b) Show that in the limit of low speed (small p and k) and ignoring mass/internal energy, this expression agrees with that of equation (6-23).