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 $\hbar \Im \left( \bigtriangledown \psi /m\psi \right) .$ In the case of one specific non-differentiable weak solution $\Psi$ we show how Bohmian trajectories can be obtained for $\Psi$ from the trajectories of a sequence $\Psi_{n}\rightarrow \Psi.$ (For any real $t$ the sequence $\Psi_{n}\left( t,\cdot \right)$ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectors $\Psi$ in the Hilbert space on which the Schr\"{o}dinger evolution $$ acts.