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Does real and imaginary part of wavefunction carries any physical interpretation?

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    $\begingroup$ Well, physics is invariant if the wavefunction is changed by an overall phase factor. $\endgroup$ – Qmechanic Mar 29 '18 at 12:40
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A complex number $x+yi$ can be written as $re^{i\theta}$. The real and imaginary parts do not matter as much as the modulus $r\geq 0$ and phase $\theta$.

The phase factor does not on its own affect probabilities of observing something observable, since they are calculated as $|z|^2=r^2$, but when adding wavefunctions it can interfere in ways that are observable (e.g. two electron orbitals with opposite phase will produce a sum of zero, indicating that the electrons repulse each other).

As Qmechanic pointed out, physics is unchanged if everything is multiplied by an overall phase $e^{i\theta}$. So there is nothing to distinguish our standard real-imaginary coordinate system from any rotated coordinate system.

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