For values of n>>1, the probability density for a quantum mechanical particle in a 1-d box oscillates very rapidly.

Thus, a calculation of the probability of detecting such a particle in the finite interval [a to b] involves integrating over several such oscillations. If this is the case, we may approximate the quantum mechanical probability density P(x) by its average value in the interval, namely,

P_{avg}(x) = Max[P(x)]/2.

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