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A: Fachverband Atomphysik

A 16: Interaction with strong or short laser pulses I

A 16.3: Vortrag

Mittwoch, 11. März 2020, 11:45–12:00, a320

A novel method to construct analytical solutions of the Dirac Equation — •Andre Gontijo Campos — Max Planck institute for Nuclear Physics

The complexity of the structure of the Dirac equation, which is a system of four coupled differential equations, renders it very difficult to study. The number of closed-form solutions is very limited due to the intricate structure of Dirac matrices, which couple the four components of the spinorial wave function. For this reason, only highly symmetric systems can be studied by analytical means; the mathematical description of more realistic systems should be based on approximation methods such as semi-classical theory or numerical calculations. However, the smallness of the time scale of relativistic electron dynamics renders the numerical solution notoriously difficult, requiring substantial computer resources. Here, we provide a very powerful method to arrive at the sought-after general analytical solutions to the Dirac equation, which fully explores the geometry of the Lorentz group. For instance, we construct time-dependent electromagnetic fields that coherently steer the electron’s spinorial wave function to follow a given path. Moreover, we also present solutions involving a plane electromagnetic wave and a combination of generally inhomogeneous electric and magnetic fields. The newly developed solutions unravel exciting new insights on the complex quantum dynamics of relativistic electrons. The presented method constitutes an important tool with a broad range of applications.