ABSTRACT
The motion of a particle in quantum mechanics is described by a (complex) wave function, ψ(r, t), that gives the probability amplitude for finding the particle at point r at time t. The absolute value squared |ψ(r, t)|2 of the wave function times a volume element d3r is the probability of finding the particle at time t in the volume element d3r about t. Because the wave ψ(r, t) is a probability amplitude, it doesn’t tell us how any one particle will behave, but rather it tells us the behavior of a large statistical sample of particles subjected to identical conditions. We found the same situation in discussing the polarization state of the photon; we could not say with certainty how any one photon would behave when, for example, passed through a polaroid. We could only give the fraction of a large number of identical photons that passed through the polaroid, and hence only the probability that any one would pass through.
