\label{fig:pes_nfft} Scheme illustrating different discretization strategies for eq. \eqref{eq:FMM_prop_aux} in one dimension. In all the cases an initial wavepacket (green) is launched towards the left side of a simulation box of length \(L\) and discretized in \(n\) sampling points spaced by \(\Delta x\). \(A\) and \(B\) indicate the space partitions corresponding to Fig. \ref{fig:pes_sheme}. Owing to the discretization of the Fourier integrals, periodic conditions are imposed at the boundaries and the wavepacket wraps around the edges of the simulation box (red). The time evolution is portrayed together with a momentum-space representation (yellow), with spacing \(\Delta k\) and maximum momentum \(k_{\rm max}\), in three situations differing in the strategy used to map real and momentum spaces:(a) Fast Fourier Transform (FFT), (b) FFT extended with zeros (zero padding) in a box enlarged by a factor \(\alpha\), and (c) zero padding with NFFT.