The Schr-Odinger equation for the wave functions is used to derive a linear partial differential equation for the time-dependent probability densities, [formula omitted], where [formula omitted] are the time-dependent position, energy, and current densities, respectively. In the limiting case where the system is in the [formula omitted] quantum state, it is shown that this partial differential equation reduces to the previously derived third-order ordinary differential equation for the probability position density. © 1969, American Association of Physics Teachers. All rights reserved.