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Fizyka --- Wszechświat. --- Filozofia --- Prognozy.

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This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.

Physics - General --- Physics --- Physical Sciences & Mathematics --- Engineering mathematics. --- Computer science --- Chemistry. --- Numerical and Computational Physics, Simulation. --- Mathematical and Computational Engineering. --- Computational Mathematics and Numerical Analysis. --- Theoretical and Computational Chemistry. --- Mathematics. --- Physical sciences --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Physics. --- Applied mathematics. --- Computer mathematics. --- Chemistry, Physical and theoretical. --- Natural philosophy --- Philosophy, Natural --- Dynamics --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Fizyka. --- Fizyka matematyczna. --- Fizyka --- informatyka.

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One-dimensional quantum systems show fascinating properties beyond the scope of the mean-field approximation. However, the complicated mathematics involved is a high barrier to non-specialists. Written for graduate students and researchers new to the field, this book is a self-contained account of how to derive the exotic quasi-particle picture from the exact solution of models with inverse-square interparticle interactions. The book provides readers with an intuitive understanding of exact dynamical properties in terms of exotic quasi-particles which are neither bosons nor fermions. Powerful concepts, such as the Yangian symmetry in the Sutherland model and its lattice versions, are explained. A self-contained account of non-symmetric and symmetric Jack polynomials is also given. Derivations of dynamics are made easier, and are more concise than in the original papers, so readers can learn the physics of one-dimensional quantum systems through the simplest model.

Electronic structure --- Matrix inversion. --- Many-body problem. --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Mechanics, Analytic --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- Matrices --- Structure, Electronic --- Atomic structure --- Energy-band theory of solids --- Mathematical models. --- Generalized inverses --- Fizyka statystyczna. --- Kwantowa teoria wielu ciał. --- Macierze (matematyka) --- Struktura elektronowa --- odwracanie. --- modele matematyczne. --- Matrix inversion --- Many-body problem --- Mathematics model --- Mathematics model.