From the above, we identify M ẋ = ∂S(x, t)/∂x as the velocity field for the quantum trajectories (since we deal with one nuclear degree of freedom we remove all dependencies on the index ν). Inserting the polar form of the nuclear wavefunction in the nuclear TDSE (4), and separating real and imaginary parts, one obtains quantum hydrodynamic equations for the fields ρ(x, t) and S(x, t) in an Eulerian frame of reference,