0124100 – Seminar (Numerical analysis for high-dimensional quantum dynamics)

Quantum dynamics provides the fundamental framework for describing microscopic physical systems, such as atoms and molecules, and is therefore central to modern physics, chemistry, and materials science. Numerical methods are key to understanding and predicting the behavior of complex atomic systems modeled by the time-dependent Schrödinger equation. However, specialized techniques are required to cope with several challenges inherent to this problem, including the possible unboundedness of the Hamiltonian, the unbounded spatial domain, the presence of multiple spatial and temporal scales, the high dimensionality of the system, and the need to preserve conserved quantities. This seminar explores specialized numerical techniques for addressing these challenges, along with their numerical analysis. The literature and presentations will be in English. Topics can be adapted to the mathematical background of the participants.