Now recently I have started quantum mechanics and I understood the wavefunction but I don't understand why $|Ψ|^2$ gives the probability density of a quantum particle. Is there a reason or perhaps maths behind it?
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$|\Psi(x)|^2 dx$ can be seen as a probability measure in the mathematical sense – Mathphys meister Jun 21 '20 at 12:28
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I have never heard a satisfying argument about such a deep question. Hence, the only advice I am able to provide is a comment of my former professor: "The only way to learn quantum mechanics is to repeat the math over and over. You stop when you have forgotten your initial questions." – Semoi Jun 21 '20 at 13:03
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Does this answer your question? Why is $|\Psi|^2$ the probability density? – ZeroTheHero Jun 21 '20 at 13:39
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Related question, but I'm sure there are many answers out there, so I won't say much.
I think the reason is basically that it makes sense and it works. Formally, I think it is generally considered as a postulate which makes sense only because experiments agree with it.
Karim Chahine
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