Calculate the Green function of problem 14.8 for the case of free space, for which ω = ck, where cis the speed of light in free space. Show that, in this case, the initial wave packet ψ(r, t₀) maintains its original shape and there is no dispersion.

Data from Problem 14.8.

Show that the time evolution of a wave packet ψ(r, t) can be expressed in terms of the initial form of the wave packet ψ(r, t₀) as

where G(r, t; r′, t₀) denotes the Green function or kernel of the integral and which depends on the dispersion relation ω(k),

Transcribed Image Text:

(r, t) = +∞ -∞ G(r, t; r', to) (r', to) d³r' y