Non-differentiable Bohmian trajectories

A solution $\psi$ to Schr"odinger’s equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\hbar \Im \left( \bigtriangledown \psi /m\psi \right) .$Inthecaseofonespecificnon-differentiableweaksolution$\Psi $weshowhowBohmiantrajectoriescanbeobtainedfor$\Psi $ from the trajectories of a sequence ${\mathrm{\Psi }}_n\to \mathrm{\Psi }\mathrm{.}$ (For any real $t$ the sequence ${\mathrm{\Psi }}_n(t,\cdot )$ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectors $\mathrm{\Psi }$ in the Hilbert space on which the Schr"{o}dinger evolution $% \Psi \mapsto e^{-iht}\Psi $ acts.