If the probability density function $\rho$ is:
$$\rho=\psi^{*}\psi=|\psi|^2$$
where $\psi$ is a complex wave function that is a solution to the Schrodinger equation, what are the physical dimensions of $\psi$?
surly:
$$\dim(\rho)=\dim(\psi^2)$$
$$\dim(\rho)^{1/2}=\dim(\psi)$$
But what are the dimensions of a pdf?