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The combination of theoretical physics methods, numerical mathematics and computers has given rise to a new field of physics known as "computational physics." The purpose of this monograph is to present the various methods of computational physics, in particular the methods of band theory. The first chapter of the book provides an introduction to the field and presents the theoretical foundations of band theory. In the second and third chapters the authors describe both traditional and more modern methods of band theory and include practical recommendations for their use. Methods which are discussed include APW (augmented plane wave), Green's function method, LMTO (linear method of MT- orbitals), LKKR (linear Korringer, Kohn and Rostocker method), LAPW (linear augmented plane wave), ASW (augmented spherical waves), and LASO (linear method of augmented Slater orbitals). Great attention is paid to the practical aspects of these theories and the book is structured in such a way as to enable the reader to use any method in practice without reference to other sources.
During the past 20 years, solid state physics has become one of the major branches of physics. 1-2 Today over one-third of all scientific articles published in physics deal with solid state 3 topics. During the last two decades, there has also been ra~id growth of scientific computation in a wide variety of fields. -5 The combination of solid state physics and comp~tation may be termed computational solid state physics. This emerging field is distin guished from theoretical solid state physics only to the extent that electronic computers rather than slide rules or backs of envelopes are used to solve numerical or logical problems, test scientific hypotheses, and discover the essential physical content of formal mathematical theories. Papers in computational solid state physics are widely scatter ed in the literature. They can be found in the traditional physics journals and review series, such as The Physical Review and Solid State Physics; in more specialized publications, such as Journal of Computational Physics, Computer Physics Communications, and Methods in Computational Physics; and in the proceedings of a number of re 6 9 cent conferences and seminar courses. - Plans for holding an International Symposium on Computational Solid State Physics in early October 1971 were formulated by Dr.
This textbook introduces modern techniques based on computer simulation to study materials science. It starts from first principles calculations enabling to calculate the physical and chemical properties by solving a many-body Schroedinger equation with Coulomb forces. For the exchange-correlation term, the local density approximation is usually applied. After the introduction of the first principles treatment, tight-binding and classical potential methods are briefly introduced to indicate how one can increase the number of atoms in the system. In the second half of the book, Monte Carlo simulation is discussed in detail. Problems and solutions are provided to facilitate understanding. Readers will gain sufficient knowledge to begin theoretical studies in modern materials research. This second edition includes a lot of recent theoretical techniques in materials research. With the computers power now available, it is possible to use these numerical techniques to study various physical and chemical properties of complex materials from first principles. The new edition also covers empirical methods, such as tight-binding and molecular dynamics.
During the past few years, there has been dramatic progress in theoretical and computational studies of large molecules and local ized states in solids. Various semi-empirical and first-principles methods well known in quantum chemistry have been applied with considerable success to ever larger and more complex molecules, including some of biological importance, as well as to selected solid state problems involving localized electronic states. In creasingly, solid state physicists are adopting a molecular point of view in attempting to understand the nature of electronic states associated with (a) isolated structural and chemical defects in solids; (b) surfaces and interfaces; and (c) bulk disordered solids, most notably amorphous semiconductors. Moreover, many concepts and methods already widely used in solid state physics are being adapted to molecular problems. These adaptations include pseudopotentials, statistical exchange approxi mations, muffin-tin model potentials, and multiple scattering and cellular methods. In addition, many new approaches are being de vised to deal with progressively more complex molecular and local ized electronic state problems.
This is the first book to present both classical and quantum-chemical approaches to computational methods, incorporating the many new developments in this field from the last few years. Written especially for "non"-theoretical readers in a readily comprehensible and implemental style, it includes numerous practical examples of varying degrees of difficulty. Similarly, the use of mathematical equations is reduced to a minimum, focusing only on those important for experimentalists. Backed by many extensive tables containing detailed data for direct use in the calculations, this is the ideal companion for all those wishing to improve their work in solid state research.
Uses the pedagogical tools of computational physics that have become important in enhancing physics teaching of advanced subjects such as solid state physics Adds visualization and simulation to the subject in a way that enables students to participate actively in a hand-on approach Covers the basic concepts of solid state physics and provides students with a deeper understanding of the subject matter Provides unique example exercises throughout the text Obtains mathematical analytical solutions Carries out illustrations of important formulae results using programming scripts that students can run on their own and reproduce graphs and/or simulations Helps students visualize solid state processes and apply certain numerical techniques using MATLAB®, making the process of learning solid state physics much more effective Reinforces the examples discussed within the chapters through the use of end-of-chapter exercises Includes simple analytical and numerical examples to more challenging ones, as well as computational problems with the opportunity to run codes, create new ones, or modify existing ones to solve problems or reproduce certain results
Computational Approaches in Physics reviews computational schemes which are used in the simulations of physical systems. These range from very accurate ab initio techniques up to coarse-grained and mesoscopic schemes. The choice of the method is based on the desired accuracy and computational efficiency. A bottom-up approach is used to present the various simulation methods used in Physics, starting from the lower level and the most accurate methods, up to particle-based ones. The book outlines the basic theory underlying each technique and its complexity, addresses the computational implications and issues in the implementation, as well as present representative examples. A link to the most common computational codes, commercial or open source is listed in each chapter. The strengths and deficiencies of the variety of techniques discussed in this book are presented in detail and visualization tools commonly used to make the simulation data more comprehensive are also discussed. In the end, specific techniques are used as bridges across different disciplines. To this end, examples of different systems tackled with the same methods are presented. The appendices include elements of physical theory which are prerequisites in understanding the simulation methods.