  The numerical analysis of the diffraction features rendered by transmission
electron microscopy (TEM) typically relies either on classical approximations
(Monte Carlo simulations) or quantum paraxial tomography (the multislice method
and any of its variants). Although numerically advan- tageous (relatively
simple implementations and low computational costs), they involve important
approximations and thus their range of applicability is limited. To overcome
such limitations, an alternative, more general approach is proposed, based on
an optimal combination of wave-packet propagation with the on-the-fly
computation of associated Bohmian trajectories. For the sake of clarity, but
without loss of generality, the approach is used to analyze the diffraction of
an electron beam by a thin aluminum slab as a function of three different
incidence (work) conditions which are of interest in electron microscopy: the
probe width, the tilting angle, and the beam energy. Specifically, it is shown
that, because there is a dependence on particular thresholds of the beam
energy, this approach provides a clear description of the diffraction process
at any energy, revealing at the same time any diversion of the beam inside the
material towards directions that cannot be accounted for by other conventional
methods, which is of much interest when dealing with relatively low energies
and/or relatively large tilting angles.
