Instead of deriving further evolution equations in the form of a potential network one can directly write down a system of coupled equations for $\psi$ (the conditional evolution equation), $\psi',\psi''$ etc. This was first noted in ^[1], a numerical realization can be found in ^[2] (Appendix A). We write \begin{equation} \psi^{(i)}(t,x) = \nabla_y^i\Psi|_{y=Y(t)} \end{equation} and get \begin{equation} \mathrm{i}\hbar\partial_t \psi^{(i)} = -\frac{\hbar^2}{2m} \left( \Delta_x\psi^{(i)} + \psi^{(i+2)}\right) + \sum_{k=0}^i {i \choose k} \left.\left( \nabla_y^k V \right)\right|_{y=Y(t)} \psi^{(i-k)} + \mathrm{i}\hbar \dot{Y}(t) \psi^{(i+1)}. \end{equation}