From Bohmian Mechanics

[edit] Welcome to Bohmian mechanics

N particles with i-th particle having mass $m i$

$\frac{d\boldsymbol{Q}_{k}}{dt} = \frac{\hbar}{m_{k}} \mathrm{Im} \frac {(\psi, \nabla_{k} \psi )} { ({\psi}, {\psi})} (\boldsymbol{Q}_1,\ldots, \boldsymbol{Q}_N) =: v_k^{\psi} (Q) \quad k= 1,\ldots,N$

Schrödinger's equation:

$i \hbar \frac{\partial \psi(\mathbf{q},t)}{\partial t} = \sum_{k=1}^N \frac{-\hbar^2}{2 m_k} \nabla^2 \psi(\mathbf{q},t)+ V(\mathbf{q}) \psi(\mathbf{q},t)$ ,

where the wavefunction $\psi(\mathbf{q},t)$ is a complex function on the configuration space variable $\mathbf{q}=(q_1, q_2, \ldots, q_N), \quad q_i \in \mathbb{R}^3$ and time t.