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I wonder what is the reason for wave function in quantum mechanics to have an imaginary part... How do we interpret the utility of the imaginary part?! As we know the wave function it self does not have any physical meaning but why should it have an imaginary part as well?

P.A.M
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    Although there are good reasons for complex wavefunctions, the modulus and phase are a more interesting parameterization thereof than are the real and imaginary parts. For example, see this calculation: https://en.wikipedia.org/wiki/Probability_current#Connection_with_classical_mechanics – J.G. May 28 '17 at 07:12

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