Numerical Methods for Quantum Dynamics (Sommersemester 2008)
- Dozent*in: Prof. Dr. Tobias Jahnke
- Veranstaltungen: Vorlesung (1608)
- Semesterwochenstunden: 2
- Hörerkreis: Mathematik und Physik (ab 5. Semester)
The lecture will be mainly based on the (yet unpublished) book
Christian Lubich: From quantum to classical molecular dynamics: reduced models
and numerical analysis, to appear, 2008, Springer, New York.
Preprints of some chapters can be downloaded from
http://na.uni-tuebingen.de/~lubich/chap1.pdf
http://na.uni-tuebingen.de/~lubich/chap2.pdf
| Termine | ||
|---|---|---|
| Vorlesung: | Donnerstag 8:00-9:30 | Seminarraum 33 |
| Lehrende | ||
|---|---|---|
| Dozent | Prof. Dr. Tobias Jahnke | |
| Sprechstunde: | ||
| Zimmer 3.042 Kollegiengebäude Mathematik (20.30) | ||
| Email: tobias.jahnke@kit.edu | ||
Quantum mechanics is full of contradictions. Its surprising implications have puzzled generations of scientists, and its various counter-intuitive consequences have raised many scientific and philosophical questions. Since the emergence of quantum mechanics in the 1920s, its correct interpretation has been debated, and the incompatibility with, e.g. the theory of general relativity, has often
been pointed out. Nevertheless, quantum mechanics has proven very successful to explain many features of the subatomic world, because often the behaviour of electrons, protons, neutrons, or photons can only be understood if quantum effects are taken into account.
From the point of view of numerical analysis, quantum dynamics represents a formidable challenge. The main numerical difficulty is the fact that the fundamental equation of motion the famous Schroedinger equation is a partial differential equation in a extremely high-dimensional space. This has motivated many approaches to replace the full Schroedinger equation by new equations of
motion which are computationally feasible but still provide an acceptable approximation. In this lecture, several of these reduced models will be presented. The presentation concentrates on the following questions:
In which sense and how well do the reduced models approximate the solution of the full Schroedinger equation?
How can the new differential equations be efficiently solved?
Many of the presented methods and techniques (such as, e.g. scale separation, splitting methods, or variational approximation) are also important in other application areas.
The course is suited for everybody with a basic background in analysis, linear algebra and numerical methods for differential equations. Knowledge in quantum mechanics is not required, since a short introduction is provided in the first weeks of the course.
Literaturhinweise
The lecture will be mainly based on the (yet unpublished) book
Christian Lubich: From quantum to classical molecular dynamics: reduced models
and numerical analysis, to appear, 2008, Springer, New York.
Preprints of some chapters can be downloaded from
http://na.uni-tuebingen.de/~lubich/chap1.pdf
http://na.uni-tuebingen.de/~lubich/chap2.pdf
The number of monographs on quantum mechanics is very large, and the following list is only a very small selection. Please feel free to discover your own favourite book.
B. Thaller, Visual Quantum Mechanics, Springer, New York, 2000.
S. Brandt & H.D. Dahmen, The Picture Book of Quantum Mechanics, 3rd ed.,
Springer, New York, 2001.
A. Messiah, Quantum Mechanics, Dover Publ., New York, 1999 (reprint of the
two-volume edition published by Wiley, 19611962).
S.J. Gustafson & I.M. Sigal, Mathematical Concepts of Quantum Mechanics,
Springer, Berlin, 2003.
D.J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective,
University Science Books, Sausalito, 2007.