The expression obtained by this procedure is a real function. Thus, in many instances we will use the
product ψ * ψ instead of ψ
2 , although if ψ is real, the two are equivalent.
For a system of particles, there is complete certainty that the particles are somewhere in the system. The
probability of fi nding a particle in a volume element, d τ , is given by ψ * ψ d τ so that the total probabil-
ity is obtained from the integration