Derivation of the probability rule

A derivation of the rule that states that ${\psi }^{*}\left(\overline{x}\right)\psi \left(\overline{x}\right)$ is the coordinate probability distribution at the space-time point $\overline{x}$ in quantum mechanics is presented. A coordinate-measuring experiment involving two light pulses that overlap at a prescribed space-time point is employed. A classical charged particle would reveal itself by absorbing energy from each pulse and reemitting a light wave whose energy and direction can be measured. In order to repeat this experiment a large number of times, the wave function must be separated into a number of identical copies. Since the (nonrelativistic) Schrödinger equation conserves $\int {\psi }^{*}\left(\overline{x}\right)\psi \left(\overline{x}\right)d^{3}x$, this separation is such that repeated measurements will give coordinates with a distribution proportional to ${\psi }^{*}\left(\overline{x}\right)\psi \left(\overline{x}\right)$.