From equation (6-33), we concluded that the group velocity of a matter wave group equals t...

From equation (6-33), we concluded that the group velocity of a matter wave group equals the velocity vn. of the massive particle with which it is associated. However, both the dispersion relation used to show that  and  used to relate this to the particle velocity are relativistically incorrect. It might be argued that we proved what we wished to prove by making an even number of mistakes.

(a) Using the relativistically correct dispersion relation given in Exercise 41, show that the group velocity of a wave pulse is actually given by

(b) The fundamental relationship  is universally correct, so  is indeed the particle momentum p. (It is not well defined, but this is its approximate, or central, value.) Making this substitution in the expression for V from part (a), then using the relativistically correct relationship between momentump and particle velocity v, show that the group velocity again is equal to the particle velocity.