(a) Write down the time-dependent Schrdinger equation in momentum space, for a free particle, and solve it....

(a) Write down the time-dependent “Schrödinger equation” in momentum space, for a free particle, and solve it.
(b) Find ϕ (p,0) for the traveling gaussian wave packet (Problem 2.42), and construct ϕ (p,0) for this case. Also construct |ϕ (p,0)|², and it is independent of time.
(c) Calculate (p) and (p²) by evaluating the appropriate integrals involving Φ, and compare your answers to Problem 2.42.
(d) Show that (H) = (p)² /2m + (H)₀ (where the subscript 0 denotes the stationary gaussian), and comment on this result.

Transcribed Image Text:

exp(-ip-t/2mh) (p.0).