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

#### Haynes Kwon

Gold Member
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?

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#### 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

Gold Member
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

#### DarMM

Science Advisor
Gold Member
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.