If you don’t know what a complex conjugate is, read this. Basically, if I have a function Ψ(x) which has a “real” part ψr(x) and an imaginary part ψi(x), with the ψ’s being real valued functions, so Ψ(x) = ψr(x) +i*ψi(x)), then multiplying Ψ(x) by its complex conjugate (Ψ*(x) = ψr(x) – i*ψi(x) , where i =√(-1) ) yields:
which (using basic algebra’s FOIL method)
ψr2(x) + ψi2(x)
Which is real valued, as the ψ’s are real valued.
This is the basis for the ‘joke’. And its funny … really …