(a) Write down the time dependent Schrdinger equation in momentum space, for a free particle, and solve it (b) Find (p,0) for the traveling gaussian wave packet (Problem 2 42), and construct (p,0) for this case Also construct (p,0) 2 , and it is independent of time (c) Calculate (p) and (p 2 ) by evaluating the appropriate integrals involving , 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 exp( ip t 2mh) (p 0)

Question: (a) Write down the time-dependent Schrdinger equation in momentum space, for a free particle, and solve it. (b) Find (p,0) for the traveling gaussian

(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.

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

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