Consider a 1D problem for a particle of mass m that is free to move in the interval z [0, a]. The potential V(x) is zero in this interval and infinite elsewhere. For that system consider a solution of the Schrdinger equation of the form NT = N sin (re-ion(t) T = [0, a], a 1 and (x, t) = 0 for x < 0 and > a. Here n 1 is an integer. (a) Find the expression for the (real) phase (t) so that the above wavefunction solves the Schrdinger equation. Find the normalization constant N. (b) Use V, (1, 0) to calculate (r), (x), and Ar. n (c) Use V,(,0) to calculate (p), (p), and Ap. (d) Is the uncertainty inequality satisfied? Is it saturated? (e) What answers in (b) and (c) change for V(x, t)? Explain.