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Zbl 1160.81001
Lubich, Christian
From quantum to classical molecular dynamics: Reduced models and numerical analysis. (English)
[B] Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society (EMS). ix, 144~p. EUR~32.00 (2008). ISBN 978-3-03719-067-8/pbk

Mechanics as a whole, classical or otherwise, is of vital value for our clear comprehension of the universe. Newtonian approaches are still important in proper contexts while it is quantum dynamics that throws light on the ultimate building blocks of matter and radiation together with the nature and features of the forces between the objects of observation and study. Investigation of the eventual passage from quantum to classical molecular dynamics is a very rich field. Particularly work with appropriate models do play immensely important a role in our attempts to master the dynamics at the various levels.\par The book under review is of 144 pages, with 5 chapters and a bibliography of 126 items. There are 9 figures and an index. It is essentially all about certain tools and techniques for exploring to understand the nature. Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts and the book is intended to help directly in this task.\par The first chapter discusses the quantum and classical dynamics and the second chapter deals with some reduced models via variational approximations. The third chapter is on numerical methods for the time-dependent Schrödinger equation whereas the ensuing one covers matters on numerical methods for nonlinear reduced models. Finally we have discussions on some semi-classical dynamics using the well-known Hagedorn wave packets.\par On the whole the author's efforts here do deserve to be fully appreciated. The work meets well with the need to explore and master the relevant computational methods and various challenges of the day.
[Paninjukunnath Achuthan (Madras)]

MSC 2000:: *81-02 Research monographs (quantum theory)
82-02 Research monographs (statistical mechanics)
70-02 Research monographs (mechanics of particles and systems)
81V55 Appl. of quantum theory to molecular physics

Keywords: quantum molecular dynamics

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