(a) Write down the time-dependent “Schrodinger equation” in momentum space, for a free particle, and solve it. Answer: exp(‒ip2t/2mћ) Φ (p, 0).
(b) Find Φ(p, 0) for the traveling gaussian wave packet (Problem 2.43), and construct Φ(p, t) for this case. Also construct |Φ(p, t)|2, and note that it is independent of time.
(c) Calculate (p) and (p2) by evaluating the appropriate integrals involving Φ, and compare your answers to Problem 2.43.
(d) Show that (H) = (p)2/2m + (H)0 (where the subscript 0 denotes the stationary gaussian), and comment on this result.
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