# Probability is square of amplitude or it's product with complex conjugate?

1. Jan 21, 2010

### zonde

I have seen discussion about it here but it is still not clear to me whether probability is square of probability amplitude or is it product of amplitude with it's complex conjugate.
I looked in HyperPhysics http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/qm.html#c5" and it says it's product with complex conjugate but I'm still not sure.

Because square and product with complex conjugate give different results.
(a+ib)^2=a^2-b^2+2iab
but (a+ib)(a-ib)=a^2+b^2

Last edited by a moderator: Apr 24, 2017
2. Jan 21, 2010

### Aganju3009

I think that probability is a real number number. If you take the square of a complex number, (a+ib)^2 you obtain a new complex number a^2-b^2+2iab. However, the product
(a+ib)(a-ib)=a^2+b^2, produces a real number.

Last edited by a moderator: Apr 24, 2017
3. Jan 21, 2010

### zonde

Aganju3009,
that should be so.
And I think I start to understand from where comes my confusion about amplitude squared thing.
In wikipedia it says: "In quantum mechanics, a probability amplitude is a complex number whose absolute value squared represents a probability or probability density."
So it's not probability amplitude squared but absolute value of probability amplitude i.e. |(a+ib)|^2. And absolute value of complex number would be length of the vector in complex plane i.e. square root from (a^2+b^2).