  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 $% \Psi \mapsto
e^{-iht}\Psi $ acts.
