\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. 