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Non-differentiable Bohmian trajectories

A solution $ψ$ to Schrödinger'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 $\hbar \Im \left( \bigtriangledown ψ/mψ\right) .$ In the case of one specific non-differentiable weak solution $Ψ$ we show how Bohmian trajectories can be obtained for $Ψ$ from the trajectories of a sequence $Ψ_{n}\rightarrow Ψ.$ (For any real $t$ the sequence $Ψ_{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 $Ψ$ in the Hilbert space on which the Schrödinger evolution $% Ψ\mapsto e^{-iht}Ψ$ acts.