/sci/ - Science & Math » Thread #11036513

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Anonymous Sun 06 Oct 11:07:32 2019 No.11036513 View Reply Original Report

Quoted By: >>11036945 >>11036968 >>11036982

how to derive probability from the wave function?

how did they come up with the modulus squared procedure? just guess it like they did with the schrodinger equation?

Anonymous

Anonymous Sun 06 Oct 2019 13:02:53 No.11036678 Report

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Anonymous

Anonymous Sun 06 Oct 2019 14:35:58 No.11036829 Report

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https://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/

Anonymous

Anonymous Sun 06 Oct 2019 15:37:38 No.11036945 Report

Quoted By:

>>11036513
The l2 norm is the only lp norm which corresponds to an inner product, I believe (see parallelogram law/polarization identity). Though there might be some other non-lp class norm which satisfies the parallelogram law, hence has an associated inner product. I'm not sure what rules those possibilities out, though my gut instinct tells me that 1) isomorphism of all (separable) Hilbert spaces and 2) Riesz representation theorem takes care of this.

Anonymous

Anonymous Sun 06 Oct 2019 15:51:09 No.11036968 Report

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>>11036513
First, complex numbers are closed. Every polynomial equation of degree n has exactly n solutions. That's what makes them so special. In order to impose the probabilistic interpretation onto complex numbers, you'll have to use the l^2 norm to make sure you'll only ever get real values.

Anonymous

Anonymous Sun 06 Oct 2019 16:00:39 No.11036982 Report

Quoted By:

>>11036513
>how did they come up with the modulus squared procedure?
Born's rule? They started using it because it matched predictions, it doesn't get derived from anywhere if that's what you're wondering

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