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From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis
Christian Lubich, University of Tübingen, Germany
A publication of the European Mathematical Society.
cover
Zurich Lectures in Advanced Mathematics
2008; 156 pp; softcover
Volume: 12
ISBN-10: 3-03719-067-1
ISBN-13: 978-3-03719-067-8
List Price: US$39
Member Price: US$31.20
Order Code: EMSZLEC/12
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Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations.

This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrödinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in quantum dynamics.

Table of Contents

  • Quantum vs. classical dynamics
  • Reduced models via variational approximation
  • Numerical methods for the time-dependent Schrödinger Equation
  • Numerical methods for non-linear reduced models
  • Semi-classical dynamics using Hagedorn Wave packets
  • Bibliography
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