Time Dependent Schrodinger Equation and Variance of Conditional Momentum

  In this note, we wish to examine how the variance of u(x)= [Sum over p p fp exp(ipx)] / [ Sum over p fp exp(ipx)]  namely: P(x) Conditional Variance(p) changes as one moves from one point to another. If one tries to eliminate u(x) from the first order change, one obtains d/dx P(x) = 2 u(x) P(x) which is a quantum mechanical result. This also leads to the change in the variance depending only on the force and kinetic energy. d/dx P(x)=2 u(x) P(x) also dictates how Shannon’s spatial entropy changes from point to point. Thus, it seems that the time-independent Schrodinger equation may be thought of in terms of changes in entropy density. The ideas here are a little different from those of (1).