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According to my knowledge (which is feeble) we will also get the same result if used direct values. For example, if the probability of something happening is 4% or 0.04, we should make an arrow of 0.04 length, but we make one of 0.02, why?

Qmechanic
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John_Nash
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    Exact duplicate of : http://physics.stackexchange.com/q/57595/ –  Sep 17 '16 at 22:19
  • Just to be clear, Feynman uses real value amplitudes in his book examples, and I think he avoids complex numbers, but in actual life, complex valued amplitudes are the norm, so to get a value that corresponds with real life, you need a real, non complex, number. Squaring does that. –  Sep 17 '16 at 22:34
  • Possible duplicates: http://physics.stackexchange.com/q/116595/2451 , http://physics.stackexchange.com/q/73329/2451 and links therein. – Qmechanic Sep 17 '16 at 23:02
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    Partly because, mathematically, wavefunctions are vectors in a $L^2$ Hilbert space, which is complex-valued. Squaring the amplitude, rather $\Psi^{*} \Psi = |\Psi|^2$ is one way to ensure that you get real-valued probabilities, which is also related to the fact that according to Sturm-Liouville theory (of which the Schrodinger equation is of such a form), the S-L operator yields real eigenvalues, and so on... – Dr. Ikjyot Singh Kohli Sep 17 '16 at 23:05
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    @IkjyotSinghKohli thanks very much for that, I always wanted to connect this point to math in a more formal way, because there is often some subtle aspect I fall over on. –  Sep 17 '16 at 23:19
  • One does not ask why the fundamental laws of physics take one form instead of the other. The machinery of QM is self-consistent and it happens to describe all so far observed phenomena (except for gravity). Therefore, the productive attitude would be to it for granted. It might of course turn out to have a domain of validity in the future. – Prof. Legolasov Sep 18 '16 at 02:52
  • @SolenodonParadoxus Well, QM is not completely self-consistent. Groenewold and von Hove's famous theorem says so. – Dr. Ikjyot Singh Kohli Sep 18 '16 at 03:11
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    @CountTo10 NP. Yes, I very much agree. – Dr. Ikjyot Singh Kohli Sep 18 '16 at 03:13
  • @IkjyotSinghKohli (correct me if I am wrong) Groenewold-van Hove's result is largely ignored since it does not imply the inconsistency of QM, but rather is an artifact of (unphysical) extra conditions which we impose on the system, like the infiniteness of space. Anyway, I hardly imagine the OP's question being about these matters. – Prof. Legolasov Sep 18 '16 at 04:11
  • but we square the value OF the arrow, so if I have a probability in the form of a complex number, won't I have to square root it to represent it in the arrow ? how will this result in non-complex numbers as the final result ? – John_Nash Sep 18 '16 at 04:51

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