Об уравнении для плотности вероятности

Abstract

The stationary Schrodinger equation depending on spatial coordinates has been considered. The problem of obtaining a differential relationship for the wave function squared was posed. By extracting Schrodinger's equation itself from this relationship a differential equation for a physically interpretable quantity, i.e. the probability density (wave function squared), has been formulated. As an example the one-dimensional case admitting a simple analytic solution was considered. The solution obtained is shown to be a solution squared of the corresponding nonlinear differential equation for the probability density. In the final section a more general non-stationary case was considered for the potential involving a time-dependent term, such potentials are found in the non-stationary perturbation theory. The constant in separating the variables remains real. Thus the procedure considered proves to be similar to that presented above for the stationary equation.