A particle in one dimension is trapped between two rigid walls:

At t = 0 it is known to b e exactly at x = L /2 with certainty. What are the relative probabilities for the particle to be found in various energy eigenstates? Write down the wave function for t ≥ 0. (You need not worry about absolute normalization, convergence, and other mathematical subtleties.)

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V(x)= 0, ∞, for 0 < x < L for x <0,x > L.