In quantum mechanics when we talk about the wave nature of particles are we referring in fact to the wave function? Does the wave function describes the probability of finding a particle (ex: photons) at some location? So do the "waves" describe probabilities just the way in classical physics the electromagnetic waves describe the perturbations of the electric and magnetic fields?
Answer
No, because the wavefunctions are not waves in space. They are waves in enormous high-dimensional spaces of possibilities. If you have two particles, the wavefunction is waving in 6 dimensions (the two positions of the two particles make a six dimensional space of possibilities), if you have three particles, the wavefunction is in 9 dimensions. So it is always wrong to think of it as a wave in space, like a field.
There is a field which obeys the Schrodinger equation, but this classical field is a classical wave, like E and B, which describes many coherent bosons in the same quantum state all moving together, like a superfluid or a Bose-Einstein condensate.
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