# A novel quantum dynamical approach in electron microscopy combining wave-packet propagation with Bohmian trajectories

## TL;DR

This paper introduces a new quantum dynamical method combining wave-packet propagation with Bohmian trajectories to analyze electron diffraction in microscopy, offering improved accuracy over classical and existing quantum methods.

## Contribution

The authors develop a general approach that integrates wave-packet propagation with Bohmian trajectories, enabling detailed analysis of electron diffraction at various energies and angles.

## Key findings

- Provides a clear description of diffraction processes at any energy.
- Reveals beam diversion inside materials not captured by conventional methods.
- Effective for low energies and large tilting angles.

## Abstract

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.