Quantum potential and wave packet spreading

The effects of the de Broglie-Bohm quantum potential on a test particle of mass $m$ are investigated in a conformally-flat geometry. A real, nonlinear, scalar field $\Psi$ is introduced and related directly to the conformal factor and to the effective mass $M(r,t)$ of the particle. The radial acceleration of a static observer in the conformally-flat metric is negative (the field is repulsive), and the corresponding proper acceleration resembles that one of the "peak radius" where the radial probability density has a global maximum during the wave packet spreading phenomenon. The timelike radial geodesics are computed in the conformally-flat spacetime in double-null coordinates and proves to be hyperbolae in the region $r>t$.