Classical trajectories compatible with quantum mechanics

Consider any stationary Schroedinger wave equation (SWE) solution ψ(x) for a particle. The corresponding PDF on position x of the particle is pX(x) = |ψ(x)| . There is a classical trajectory x(t) for the particle that is consistent with this PDF. The trajectory is unique to within an additive constant corresponding to an initial condition x(0). However the value of x(0) cannot be known. As an example, a free particle in its ground state in a box of length L obeys a classical trajectory x/L− (1/2π) sin(2πx/L) + t0 = t. The constant t0 is an unknowable time displacement. Momentum values, however, cannot be determined by merely differentiating d/dt the trajectory x(t) and, instead, follow the usual quantification rules of Heisenberg’s. This permits position and momentum to remain complementary variables. Our approach is fundamentally different from that of D. Bohm.