Spatial Motion in Quantum Mechanics and Wavefunction Squared as Density

In a previous note, it was argued one could construct an expression for P(p/x), the probability for a momentum p at x, and then by using formulas from statistics show that physical density in quantum mechanics equals the wavefunction squared. In this argument, the wavefunction W(x) is an x dependent normalization constant for an expression of average kinetic energy at a point x, namely [Sum on p p*p/2m fp sin(px)] / W(x). Here fp is a probability weight to have a momentum p and it was noted that W(x) and fp are Fourier transforms of each other. In this note, we wish to attempt to examine two points. First, it seems a little confusing that one sums over all possible momenta at a point x . We would like to see if there could be a reason for this. Secondly, we wish to obtain the result: spatial density = wavefunction squared in terms of a picture of dynamics so that there is some idea of what is happening at a microscopic level in quantum mechanics