In quantum mechanics, [tex]\psi^2[/tex] the basic wave function has no physical meaning or significance. However, [tex]|\psi|^2[/tex] represents the probability distribution of particle in a given space.
Probability [tex]\propto[/tex] [tex]|\psi|^2[/tex]
So when you will put a position and a time in [tex]\psi^2[/tex] function, it will give you the probability of finding the particle at that particular position and at the given time.
