  Non-relativistic de Broglie-Bohm theory describes particles moving under the
guidance of the wave function. In de Broglie's original formulation, the
particle dynamics is given by a first-order differential equation. In Bohm's
reformulation, it is given by Newton's law of motion with an extra potential
that depends on the wave function--the quantum potential--together with a
constraint on the possible velocities. It was recently argued, mainly by
numerical simulations, that relaxing this velocity constraint leads to a
physically untenable theory. We provide further evidence for this by showing
that for various wave functions the particles tend to escape the wave packet.
In particular, we show that for a central classical potential and bound energy
eigenstates the particle motion is often unbounded. This work seems
particularly relevant for ways of simulating wave function evolution based on
Bohm's formulation of the de Broglie-Bohm theory. Namely, the simulations may
become unstable due to deviations from the velocity constraint.
