Unformatted text preview: 2 2 2 2 mL n E n = (a) Find C for all n . (5 pts) (b) If at t = 0, ( 29 L x elsewhere L x i L x A x < < + = 3 sin 2 sin , , find A . (5 pts) (c) Find x ˆ at t = 0. (5 pts) (d) Find p ˆ at t = 0. (5 pts) (e) Derive the expression for (x,t) . (5 pts) (f) Find ) ( ˆ t E for t > 0. (5 pts) Prob. 4.4. Following the description of Prob. 4.3 of the infinitepotential well, if at t = 0, the particle is only in the ground and first excited states with equal probability, (a) Find (x,0) with proper normalization. (5 pts) (b) Find P(x,t) and sketch P(x,t) against x for a few t ’s to show the motion. (5 pts) (c) Find x ˆ and p ˆ at t = 0. (10 pts) (d) Find x dt d (5 pts) (e) Find ) ( ˆ t E for t > 0. (5 pts) 1...
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 '09
 KAN
 pts, Eigenvalue, eigenvector and eigenspace, Fundamental physics concepts, 2m, Eigenfunction

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