Intuition behind probability amplitude calculations?

[sciencegem]

Why is the probability of a particle being at a certain location proportional to the square of of "the" amplitude? What does "the" in that sentence represent more specifically? Why are amplitudes complex numbers? Any intuition or clarification would be very appreciated.
Thanks!

 

[vanhees71]

It's one of the fundamental postulates of quantum theory that the probability distribution for the position is given by the modulus squared of the wave function, which is most easily formulated as a complex valued function. You can only give some heuristical (or better historical) arguments to understand, where this postulate by Born comes from. For a quite deep discussion see the very good newest textbook

S. Weinberg, Quantum Mechanics, Cambridge University Press