Numerical Analysis for High-dimensional Quantum Dynamics

What it is about

You learn mathematical foundations and numerical methods for simulating quantum-dynamical systems in high dimensions. In the module you treat grid-based methods, the Truncated-Wigner Approximation, the time-dependent variational principle methodology, and the Gaussian wave packet approximation. In the end you will be able to understand and apply central approximations in phase-space formulation and methods from the time-dependent variational principle.

What you will be able to do

• Understand mathematical foundations of quantum dynamics
• Apply grid-based numerical methods
• Analyze the Truncated-Wigner Approximation
• Apply the time-dependent variational principle
• Apply Gaussian wave packet approximation
• Evaluate approximations in classical phase space

What the module consists of

• VorlesungPresentation of the content with examples and discussion to convey the theory
• Übung/Practice sessionsDeepening the content through worksheets, initially guided, later increasingly autonomous

Teaching method

• Lecture with examplesto present the concepts and motivate independent engagement
• Discussion with studentsto clarify and deepen the content
• Practice sessions with exercises and solutionsto practice methods and to self-check learning progress