Computation In Modern Physics (Third Edition)
Computation In Modern Physics (Third Edition)

Author: William R Gibbs

Publisher: World Scientific Publishing Company

Published: 2006-05-05

Total Pages: 380

ISBN-13: 9813106700

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This textbook is suitable for two courses in computational physics. The first is at an advanced introductory level and is appropriate for seniors or first year graduate students. The student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, linear algebra, finite element techniques, digital signal processing and chaos. In this first part of the book, no knowledge of quantum mechanics is assumed. The third edition has expanded treatments of the subjects in each of the first nine chapters and a new section on modern parallel computing, in particular, Beowulf clusters.The second course (the last four chapters) deals with problems in the strong interaction using quantum mechanical techniques, with emphasis on solutions of many-body scattering problems and several-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with the numerical summation of divergent series.

Computation In Modern Physics (Second Edition)
Computation In Modern Physics (Second Edition)

Author: William R Gibbs

Publisher: World Scientific Publishing Company

Published: 1999-11-22

Total Pages: 374

ISBN-13: 9813105569

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The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques on the solution of complex problems is difficult to overstate. Even our approach to most problems has been changed. Solutions to problems once thought intractable are being routinely secured. Instead of using oversimplified models, as has been the practice for the treatment of scientific systems in the past, the entire problem can now be tackled successfully.The second edition of Computation in Modern Physics develops and presents algorithms for the solution of many types of mathematical systems, some dating as far as the last few centuries, but also quite a number that have been developed within the last 10-50 years. In this latter category, close attention is paid to the rapidly developing area of Monte Carlo techniques, where new conceptual views of physics problems are being brought into play. With this method, problems in a large number of dimensions can be solved through the introduction of a modern method for the representation of multidimensional functions.This invaluable book is suitable for two different levels of computational physics. The first part of the book is of an advanced introductory level and is appropriate for good students with no previous experience in computational methods or any student with some experience. Here the student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, methods of linear algebra, finite element techniques, digital signal processing and chaos.The second part of the book is more specialized for problems in strong interaction with emphasis on solutions to many-body scattering problems and several-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.

Modern Physics with Modern Computational Methods
Modern Physics with Modern Computational Methods

Author: John Morrison

Publisher: Academic Press

Published: 2020-10-13

Total Pages: 500

ISBN-13: 0128177918

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Modern Physics with Modern Computational Methods, Third Edition presents the ideas that have shaped modern physics and provides an introduction to current research in the different fields of physics. Intended as the text for a first course in modern physics following an introductory course in physics with calculus, the book begins with a brief and focused account of experiments that led to the formulation of the new quantum theory, while ensuing chapters go more deeply into the underlying physics. In this new edition, the differential equations that arise are converted into sets of linear equation or matrix equations by making a finite difference approximation of the derivatives or by using the spline collocation method. MATLAB programs are described for solving the eigenvalue equations for a particle in a finite well and the simple harmonic oscillator and for solving the radial equation for hydrogen. The lowest-lying solutions of these problems are plotted using MATLAB and the physical significance of these solutions are discussed. Each of the later chapters conclude with a description of modern developments. Makes critical topics accessible by illustrating them with simple examples and figures Presents modern quantum mechanical concepts systematically and applies them consistently throughout the book Utilizes modern computational methods with MATLAB programs to solve the equations that arise in physics, and describes the programs and solutions in detail Covers foundational topics, including transition probabilities, crystal structure, reciprocal lattices, and Bloch theorem to build understanding of applications, such as lasers and semiconductor devices Features expanded exercises and problems at the end of each chapter as well as multiple appendices for quick reference

Computational Physics
Computational Physics

Author: Jos Thijssen

Publisher: Cambridge University Press

Published: 2007-03-22

Total Pages: 637

ISBN-13: 0521833469

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First published in 2007, this second edition is for graduate students and researchers in theoretical, computational and experimental physics.

Stochastic Numerics for Mathematical Physics
Stochastic Numerics for Mathematical Physics

Author: Grigori N. Milstein

Publisher: Springer Nature

Published: 2021-12-03

Total Pages: 754

ISBN-13: 3030820408

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This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.