Physics 4307

Introduction to Quantum Mechanics

Problem 3.5 (c) and (d)---Hint 1

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

Diagram of quantum and classical square wells in 1D

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,

Pavg(x) = Max[P(x)]/2.

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