Numerical approximations in quantum dynamics

Prof. Dr. Christian Lubich

Abstract

The course treats computational approaches to molecular quantum dynamics, based on the book [1]. The first part starts with the Dirac-Frenkel time-dependent variational approximation as a basic model reduction and approximation principle and describes some of its uses such as the time- dependent Born-Oppenheimer approximation, the time-dependent multi-configuration Hartree method, and Gaussian wavepacket dynamics. The second part deals with spatial approximations based on Hermite functions, including sparse grids and hyperbolic crosses for higher-dimensional problems. The third part considers a numerical approach to semiclassically scaled Schrödinger equations that is based on Hagedorn's semiclassical wavepackets. Appropriate time discretization methods such as splitting methods and Krylov subspace methods for matrix exponentials are also treated as far as time permits.

Literature

Lubich, Christian
From quantum to classical molecular dynamics: reduced models and numerical analysis.
Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2008.
x+144 pp. ISBN: 978-3-03719-067-8

Date and Place

• 09.07.2012: 09:00 - 12:00, TUM MI 02.13.010
• 10.07.2012: 09:00 - 12:00, TUM MI 03.06.011
• 11.07.2012: 09:00 - 12:00, TUM MI 02.13.010