 Bohm then used the modified Hamilton-Jacobi equation to define particle trajectories just as one does for the classical Hamilton-Jacobi equation, that is, by identifying \(\partial_k S\) with \(m_k\boldsymbol{v}_k\), i.e., by setting   \[ d\mathbf{Q}_k /dt = \partial_k S / m_k. \]   This is equivalent to  the guiding equation  for particles without spin. [In this form the (pre-Schrödinger equation) de Broglie relation \(\boldsymbol{p} = \hslash \boldsymbol{k}\), as well as by the eikonal equation of classical optics, already suggest the guiding equation.] The resulting motion is precisely what would be obtained classically if the particles were acted upon by the force generated by the quantum potential, in addition to the usual forces.