3. A particle in an infinite square well at t=0 has a probability density that is uniform in the left half (0
3. A particle in an infinite square well at t=0 has a probability density that is uniform in the left half (0
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Transcribed Image Text:3. A particle in an infinite square well at t=0 has a probability density that is uniform in the
left half (0<x<L/2), and 0 in the right half. (This is a bit unphysical, because (x, t = 0) = 0
at the left wall of the potential well, but it makes the math easier for this question.) Assume that
(x, t = 0) is a positive, real function.
a)
Sketch (x, t = 0) and write a mathematical formula for it (e.g. a "piecewise" formula
specifying it in the regions 0<x<L/2 and L/2 < x <L). Make sure your formula is normalized!
b) Find a general formula (valid for all n) for the probability that a measurement of energy
yields En, and evaluate this formula for the first 4 cases (n = 1 to 4). Explain what happens when
n = 4 (Explain the "math" answer using a graph!)
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