I found this passage interesting and illuminating: (from Feynman's book 'QED') ".. In this example, complex numbers were multiplied and then added to produce a final amplitude for the event, whose square is the probability of the event. It is to be emphasized that no matter how many amplitudes we draw, add, or multiply, our objective is to calculate a single final amplitude for the event. Mistakes are often made by physics students at first because they do not keep this important point in mind. They work for so long analyzing events involving a single photon that they begin to think that the wavefunction or amplitude is somehow associated with the photon. But these amplitudes are probability amplitudes, that give, when squared, the probability of a complete event. Keeping this principle in mind should help the student avoid being confused by things such as the "collapse of the wavefunction" and similar magic."