Asymptotic and Computational Methods for Semiclassical Schrodinger Equations
A short lecture course by Shi Jin (University of Wisconsin-Madison and Shanghai Jiao Tong University)
4 - 5 July 2013
Organiser: Andrew Stuart
One of the main difficulties in computational quantum mechanics is the highly oscillatory nature of the wave function in the Schrodinger equation. In this course, we will introduce asymptotic and numerical methods for the Schrodinger equation in the semiclassical regime. We will use the WKB method and Wigner tranform to study the semiclassical limit, and then provide descriptions for the semiclassical limit in both the physical space (via multi-valued moment system) and in the phase space. For problems with periodic potentials we will introduce the Bloch decomposition. Numerical methods for these problems will also be discussed.
All lectures to be held in Room B3:02, Zeeman Building, Mathematics Institute, University of Warwick
Provisional Schedule:
Thursday 4 July
09:30-11:00 Lecture 1 (Shi Jin)
11:00-11:45 Coffee/Tea (Common Room)
11:45-12:45 Markus Schmuck (Renormalization and Entropy Methods for a New Stochastic Mode Reduction)
12:45-14:15 Lunch
14:15-15:45 Lecture 2 (Shi Jin)
15:45-16:30 Coffee/Tea (Common Room)
Friday 5 July
09:30-11:00 Lecture 3 (Shi Jin)
11:00-11:45 Coffee/Tea (Common Room)
11:45-12:45 Ben Goddard (Transitions Through Avoided Crossings: A Complex, Multiscale Problem)
12:45-14:15 Lunch
14:15-15:45 Lecture 4 (Shi Jin)
15:45-16:30 Coffee/Tea (Common Room)
Funded by:
MASDOC/EPSRC and Warwick IAS
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