ps03 - Homework (3) for Physics 316, Modern Physics I

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Unformatted text preview: Homework (3) for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Friday, 02/18/04 - 9:05 in 132 Rockefeller Hall Exercise 1: Replace the relativistic treatment of de Broglie which lead to p = ~ k and E = ~ with E = q ( pc ) 2 + ( mc 2 ) 2 , by a non-relativistic treatment in which E = p 2 2 m + mc 2 . This is obtained by making a second order expansion in v/c . (a) Find as a function of k and compute the phase velocity and the group velocity. (b) Does the group velocity equal the particle velocity as required? (c) Sketch phase and group velocity as a function of particle velocity v . (d) What happens to phase and group velocity when the rest energy is changed: E = p 2 2 m + E . Can the change in the phase velocity be detected experimentally by an interference experiment? Consider that an interference experiment is always sensitive the the phase difference between two waves....
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