# Partial Differential Equation for the Time-Dependent Probability Densities of Quantum Mechanics

@inproceedings{Kostin1969PartialDE, title={Partial Differential Equation for the Time-Dependent Probability Densities of Quantum Mechanics}, author={M. D. Kostin}, year={1969} }

The Schrodinger equation for the wave functions is used to derive a linear partial differential equation for the time-dependent probability densities, ħ24m δ3P(x, t)δx3 = 2V(x) δPδx + V′P(x, t) − 2δe(x, t)δx − mδj(x, t)δt, where P(x, t), e(x, t), j(x, t) are the time-dependent position, energy, and current densities, respectively. In the limiting case where the system is in the nth quantum state, it is shown that this partial differential equation reduces to the previously derived third-order… CONTINUE READING