A friend of mine recently tried to tell me that the square of the wave function for a particle (that is, [itex]\Psi^2[/itex]) gives the probability density of finding a particle in space. I disagree. I always thought that the wave function multiplied by its complex conjugate (that is, [itex]\Psi \Psi^*[/itex]) yielded the probability density for the particle. They are definitely not the same, because [itex]\forall a,b \neq 0, \ (a+bi)^2 = a^2 + 2abi + b^2 \neq a^2 + b^2[/itex]. So, is the probability density given by [itex]\Psi^2[/itex] or [itex]\Psi \Psi^* = |\Psi|^2[/itex]?