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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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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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May the paper itself be of more help.

Best Regards,

DaTario

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See, e.g., https://www.physicsforums.com/showpost.php?p=1415621&postcount=13

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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Regarding the post at https://www.physicsforums.com/showpos...1&postcount=13 [Broken], I had read that before posting my question but I was hoping for more--not just that it can be done without reference to the complex numbers, but *why* the complex numbers are appropriate, and why we choose to use them.

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https://www.physicsforums.com/showthread.php?t=287383

I have collected a lot of mathematical articles about the complex amplitude which I haven't had the time to read. But if you suggest a way to transfer files, then I can send them to you.

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The physicist M. Nussenzveig once has said that he bet if one can build quantum mechanism without complex numbers.Regarding the post at https://www.physicsforums.com/showpos...1&postcount=13 [Broken], I had read that before posting my question but I was hoping for more--not just that it can be done without reference to the complex numbers, but *why* the complex numbers are appropriate, and why we choose to use them.

Best Wishes

DaTario

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You could instead express QM by a set of coupled differential equations. However, this set included the Cauchy-Riemann equations, so it becomes quite natural to use complex numbers because those equations are automatically satisfied.but *why* the complex numbers are appropriate, and why we choose to use them.

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