Ángel S. Sanz – Instituto de Física Fundamental (IFF-CSIC)

Quantum mechanics is the most powerful tool that we have nowadays to describe the microscopic world. Its applications cover a wide range of fields of physics and chemistry, at both a fundamental and an applied level. Its language is clear and concise: given an initial state (described by the wave function) and a certain interaction (accounted for by a potential function), one obtains a final state, i.e., the response of the system to such an interaction, though the action of the Hamiltonian operator or, in a more general sense, the time-dependent Schrödinger equation. This is, maybe, a rather simplistic input-output scheme of how things work with quantum mechanics, but describes quite well its general modus operandi. Within this scheme, though, not much is said about how to interpret such states or their evolution. Actually, in case it was needed, one usually resorts to classical or semiclassical methodologies, namely classical trajectories plus added phases.

At this point, one cannot feel but frustrated: Quantum mechanics provides accurate answers to our problems, but says nothing about why they emerge in the way they do within the same theoretical framework. In other words, if quantum mechanics is regarded as a statistical theory (in the end, experimentally, in order to get a full answer one needs to perform a number of identical experiments), is it possible to count with the help of any equivalent tool to the Newtonian trajectories that we use to interpret classical statistical simulations? The answer is yes, and it is called Bohmian mechanics. Putting aside fundamental issues, such as the existence of hidden variable, the question is that quantum mechanics admits a similar treatment as classical hydrodynamics and, therefore, one can define in a natural fashion streamlines or trajectories that help us to visualize and understand the evolution of the quantum system (which is treated as “quantum flow”). More specifically, Bohmian trajectories are the equivalent, for example, to the tracks pursued by tracer particles in a liquid, when one wants to study its dynamics, though in the former case they would be “quantum tracers”.

In this talk, I will present an overview of a series of applications of this mechanics to in the field of the Atomic, Molecular and Optical (AMO) Physics, showing the physical insight that this quantum approach provides us about them and clues on different ways to understand them. In particular, I have selected a series of systems, which, to some extent, are illustrative of the kind of phenomena and effects that we may find in this field (but also in others), such as the particle diffraction/interference and atom-surface scattering, molecular reactivity, transport in waveguides, or strong-field interactions. These studies go from statistical treatments (including quantum-classical correspondence) to single-trajectory analyses.