In one of your other posts you wrote that if F = -kx and F = dP/dt, then -kx = dP/dt. This is only true for the special case when the sum of the forces on the system under consideration is equal to -kx. Newton's second law states that if you take the vector sum of all the forces acting on an object of mass m, then that sum is equal to the time derivative of the object's momentum.
I started reading through your post, and noticed that you divided both sides of the equation by the wave function, canceling the spatial part of the wave function on both sides prior to taking the derivative with respect to x of that same function. Once I got to that math error, I quit reading.