Amplitudes can be non-real, so simply squaring them doesn't ensure that you have a (non-negative) probability; you have to also take the absolute value. It's still a pretty straightforward process to derive a probability from an amplitude, but fully explaining that process is a bit of a distraction from making the point that amplitudes really aren't probabilities and shouldn't be thought of as equivalent to or even intuitively similar to probabilities.
Re:The “Talk”
by a1369209993 on Monday October 28, 2019 @09:14PM
(#21383440)
To be more pedantic, it's actually the product of [amplitude] times [complex conjugate of amplitude][0]. Confusingly, this is sometimes called the "square" of a value - usually in contexts where complex-element vectors and matrices are involved, since most[1] real-element formulas calling for matrix transpose (dot products[2] are a special case of this) actually want conjugate transpose[3] but didn't notice because conjugate is identity on reals.
0: zz* = (z)·(z*) = (a+bi)·(a-bi)
1: Possibly all - I have yet to happen across a counterexample.
2: https://en.wikipedia.org/wiki/Dot_product#Algebraic_definiti...
I'm not sure why they don't just say that, it is the most straightforward part of QM.