I Why does the square of the amplitude of a wave function represent P?

[Haynes Kwon]

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

 

[HomogenousCow]

It’s simply a postulate of quantum mechanics, you can motivate it based on various arguments but it cannot really be derived from anything in a non-circular manner.

 

[Mentz114]

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

Have a look at this post

https://www.physicsforums.com/threa...rs-in-quantum-theory-the-povm-concept.977280/

 

[DarMM]

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

It can be derived to a certain degree, but the most general such derivations are quite advanced. If you're still learning QM it is best to accept it as a postulate.

A derivation of it is basically if you acknowledge nature can have discrete outcomes in certain experiments with those outcomes having a certain algebraic relation to each other you can derive that all probabilities must come from a specific operator $\rho$ with the wavefunction being a sort of special case (pure state). See the thread @Mentz114 mentioned as well.