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Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contained in this book allow for a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, rather than just used. The same applies to some basic notions of solid state theory, as, for instance, the Fermi surface. Also, the language of second quantization is introduced systematically in an Appendix for readers without a formal theoretical physics background.

Mathematical physics --- Quantum mechanics. Quantumfield theory --- Plasma physics --- Statistical physics --- Matter physics --- Chemistry --- Materials sciences --- Computer science --- Computer. Automation --- EMI (electromagnetic interference) --- molecuulfysica --- materiaalkennis --- materie (fysica) --- plasmafysica --- quantummechanica --- theoretische fysica --- chemie --- informatica --- atoomfysica

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This book introduces the collision theory of nonrelativistic quantum systems, a standard tool for the exploration of the interaction between quantum particles and their properties. The authors cover the basic elements of the theory by a detailed discussion of elastic scattering on the basis of a stationary formulation in terms of differential and integral equations as well as a time dependent formulation leading to S-matrix theory. An extension to the treatment of inelastic processes with a many channel situation is outlined and illustrated by an application to three-body and nuclear transfer processes. Special emphasis is laid on the discussion of selection rules due to different symmetries of the interaction between the particles and the scattering of spin-polarised particles in separate chapters. Specific mathematical details are presented in separate sections at the end of each of the seven chapters in order to maintain the flow of argumentation concerning the actual aspects of the physics of collision processes. This book is a translation of the original German 1st edition Streutheorie in der nichtrelativistischen Quantenmechanik by Reiner M. Dreizler, Tom Kirchner & Cora S. Lüdde, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). The present version has been revised extensively with respect to technical and linguistic aspects by the authors. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. The Authors Reiner M. Dreizler, Professor emeritus of Theoretical Physics at Goethe University, Frankfurt/Main,works on many-body systems in quantum mechanics. Tom Kirchner, Professor of Physics at York University, Toronto, Canada, works on quantum dynamics of multi-particle Coulomb systems, in particular atomic scattering processes. Cora S. Lüdde, Diplom-physicist, research associate at Goethe University, Frankfurt/Main, Germany, working on application-oriented programming, researches computer arithmetic.

Mathematical physics --- Quantum mechanics. Quantumfield theory --- Elementary particles --- elementaire deeltjes --- quantumfysica --- theoretische fysica --- kwantumleer --- wiskunde --- fysica