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Density functional theory. An approach to the quantum many-body problem. (English) Zbl 0723.70002

Berlin etc.: Springer-Verlag. xi, 302 p. DM 148.00 (1990).
This is delightful book. In its 302 pages the authors tell a story which most authors would do in over a thousand pages. One device used for saving space is to leave concepts and objects whose precise mathematical definitions are obvious from the context undefined. The book is very timely. The theory of density functionals for approximating n-electron problems is a fashionable area in which there is much activity at the present time. As Professor Walter Kohn puts it most succinctly in the foreword: “The book’s hallmarks are clarity and - within its self- imposed limitation - completeness”.
The scheme of this well-organized book is as follows: after a very brief introduction in chapter 1, in chapter 2 the authors build the foundations of the subject. They give a clear and concise account of the Hohenberg- Kohn theorem and its extension to the degenerate ground states. In the same chapter they describe v-representability and the related question of the appropriate variational principles one must use and this leads them to consider a number of important topics, among them, fractional particle numbers, chemical potentials and discontinuities in the derivatives. In chapter 3 the theory is extended to a variety of interesting systems and ensembles. Chapter 4 explains the formalism of the Kohn-Sham scheme in some detail. Kinetic and exchange energy functionals derived from the single particle density matrix are considered in detail in chapter 5 as examples of explicit functionals. Interesting accounts of Kirzhnits method, Wigner-Kirkwood approximation, Padé approximants and classical density functionals of Thomas, Fermi, Dirac and von Weizsäcker are to be found here. Chapter 6 gives a brief account of the many-body perturbation theory. Chapter 7 tells the reader almost all that he needs to know about various local density approximations and their ramifications. Chapter 8 deals with the extension of the theory to relativistic systems.
The book contains two appendices. The first contains definitions of certain mathematically relevant objects such as density matrices, Green’s functions and correlation functions and in the second appendix the authors devise a careful scheme of giving an extremely concise and interesting comparative account of the literature on numerical computations based on the theory considered in this book and other related theories.
Throughout the book, the theory is supplemented by relevant numerical data in tabular forms constructed with great care.
The book has over 750 references in its bibliography which means that it includes every work of significance in this area.
Springer-Verlag should be congratulated for continuing improvement in the art of printing and binding books - this book is a fine example of the state of the art in these areas.

MSC:

70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
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