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I am a bit confused about something. I have been taught that wavefunctions are basicaly the square root of probability functions. I have also read that some wavefunctions are complex which means that they involve the value i which is the square root of minus one. These two things together do not make sense to me for the following reason:

The way I see it, the output value of a probability function can only be a real number between zero and one inclusive with zero representing "impossible" and one representing "certain". If the output value of a complex wavefunction is x + iy then the square of this is x^{2}+ ixy - y^{2}. For this to equal any real number between zero and one inclusive (or any other positive real number), y must be equal to zero which means that the wavefunction cannot not be complex.

What exactly do complex wavefunctions represent if not the square root of probability functions? Do complex wavefunctions represent anything meaningful and fully comprehendable in the "real" world that we perceive?

Thank you very much.

Kind regards

Tim

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# Complex wavefunctions and probability

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