Reconstruction of Bohm trajectories and wave functions from interferometric measurements

We propose a generalization of the technique of quantum state reconstruction to obtain the space derivative of the phase of a wave function, which is central to the hydrodynamic formulation of quantum mechanics in the manner of Madelung and Bohm. In this way we can construct Bohm trajectories and make contact with a recent experiment [Kocsis et al., Science 332, 1170 (2011)] extracting these trajectories after a double slit.