I'd like to know why wave functions are taken to be complex-valued in general, and where the i in the Schrödinger equation comes from and what it means. I've seen plenty of we-use-this-because-it-works type arguments. What I'm hoping for is a meaningful explanation of how the complex numbers arise out of the physics and what physical quantities (or changes of physical quantities, etc) are modeled by the real and imaginary parts of the wave function (in particular, not just the familiar interpretation of the modulus of this function). I'd appreciate any insight or perhaps just a reference to a book where this is discussed. Right now I'm reading Shankar. The physics is pulled out of nowhere.(adsbygoogle = window.adsbygoogle || []).push({});

I'm a PhD math student trying to pick up quantum mechanics. In particular, I'm a harmonic analyst if that means anything to you, but my background in physics is negligible

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# Why is wavefunction complex-valued?

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