Problem 2. (30 pts) Consider a simple model of a free particle wave packet as a "square packet". We will model this at t = 0 as: ipox (x, t = 0) = 0, x < 0 0 ≤ x ≤ a 0, x > a Aex(ax)/a², (5 pts) Write down the integral expression to determine A (but do not evaluate it). a. b. (4 pts) Sketch the real part of (x, t = 0). Assume a > h/po. (Note that A = . √30/a ). c. (7 pts) Write down the integral for the momentum-space wave function (p). Do not evaluate it, but put it into a form such that it could be evaluated by a software program (such as Mathematica). d. (4 pts) Sketch an estimate of the plot of (p) 2. Since you did not evaluate the integral in part c, you only need to include important features: location(s) of maximum value(s), the characteristic width (if relevant) and the behavior at large tp. Very briefly explain the reason for each feature. e. (4 pts) If the box width a were increased, how would that change your plot in part d? Explain. f. (6 pts) Short answers: i. Is (x) = 0 at t = 0? Briefly explain ii. Does (x) change with time? Briefly explain iii. Is (p)=0 at t = 0? Briefly explain. iv. Does (p) change with time? Briefly explain.