The unit of dx is length, so that means |ψ|2 has to be 1/length for the probability density to become dimensionless.
|ψ| must then be [length]-1/2.
Thank you :)
Oh, I see. |ψ|2 is a function and you will only get a probability if this function is integrated.
I only have a wave function for a free particle
ψ(x,0)=Ae-(x-x0)2/4a2eilx,
where a and l are constants that I don't know the dimensions of.