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I find the idea of the wave function being 'just' a collection of numbers (probabilities) quite alluring, and elegant in explaining away the whole 'collapse' business (see Luboš' answer to this question).

I realize though, you can only stretch an analogy so far. Yes, learning location of a wanted criminal does not in fact 'collapse' his wave function, but is there any analogy which explains wave function interfering with itself (as per double split experiment)?

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There isn't anything to explain, really. The results of assuming the existence of a wavefunction which can interfere with itself agree with experimental reality. –  dmckee Sep 17 '12 at 2:06
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up vote 2 down vote accepted

The wave function is a mathematical solution of a specific quantum mechanical equation different for different potentials and boundary conditions. This formulation is validated by a plethora of experimental data, not only the two slit experiment.

Since we are familiar with sound and light interference we call the mathematically similar patterns of the two slit experiment with electrons "interference" patterns.

This terminology just reflects that the probabilities in space of finding an electron on the screen are affected by the boundary condition of the two slits to create an interference pattern.The wavefunction given by the solution for "two slits and incoming electron" has the patterns.

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Guess I have to learn to live with this uncomfortable fact, and seeing how much there is to learn, the sooner, the better. –  pafau k. Sep 18 '12 at 8:47
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