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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.
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
A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
More physicists today are taking on the role of software developer as part of their research, but software development isnâ??t always easy or obvious, even for physicists. This practical book teaches essential software development skills to help you automate and accomplish nearly any aspect of research in a physics-based field. Written by two PhDs in nuclear engineering, this book includes practical examples drawn from a working knowledge of physics concepts. Youâ??ll learn how to use the Python programming language to perform everything from collecting and analyzing data to building software and publishing your results. In four parts, this book includes: Getting Started: Jump into Python, the command line, data containers, functions, flow control and logic, and classes and objects Getting It Done: Learn about regular expressions, analysis and visualization, NumPy, storing data in files and HDF5, important data structures in physics, computing in parallel, and deploying software Getting It Right: Build pipelines and software, learn to use local and remote version control, and debug and test your code Getting It Out There: Document your code, process and publish your findings, and collaborate efficiently; dive into software licenses, ownership, and copyright procedures
Eine gut verständliche Einführung in moderne naturwissenschaftliche Rechenmethoden! Nur geringe physikalische Vorkenntnisse voraussetzend, vermittelt der Autor Grundlagen und komplexere Ansätze anhand vieler Beispiele und ausgesprochen praxisnaher Übungsaufgaben. Besprochen werden alle Rechenmethoden, die im Grundstudium erlernt werden sollen, hinsichtlich ihrer Leistungsfähigkeit und ihrer Anwendungsgebiete.
The use of computation and simulation has become an essential part of the scientific process. Being able to transform a theory into an algorithm requires significant theoretical insight, detailed physical and mathematical understanding, and a working level of competency in programming. This upper-division text provides an unusually broad survey of the topics of modern computational physics from a multidisciplinary, computational science point of view. Its philosophy is rooted in learning by doing (assisted by many model programs), with new scientific materials as well as with the Python programming language. Python has become very popular, particularly for physics education and large scientific projects. It is probably the easiest programming language to learn for beginners, yet is also used for mainstream scientific computing, and has packages for excellent graphics and even symbolic manipulations. The text is designed for an upper-level undergraduate or beginning graduate course and provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. As part of the teaching of using computers to solve scientific problems, the reader is encouraged to work through a sample problem stated at the beginning of each chapter or unit, which involves studying the text, writing, debugging and running programs, visualizing the results, and the expressing in words what has been done and what can be concluded. Then there are exercises and problems at the end of each chapter for the reader to work on their own (with model programs given for that purpose).
Quantum mechanics undergraduate courses mostly focus on systems with known analytical solutions; the finite well, simple Harmonic, and spherical potentials. However, most problems in quantum mechanics cannot be solved analytically. This textbook introduces the numerical techniques required to tackle problems in quantum mechanics, providing numerous examples en route. No programming knowledge is required – an introduction to both Fortran and Python is included, with code examples throughout. With a hands-on approach, numerical techniques covered in this book include differentiation and integration, ordinary and differential equations, linear algebra, and the Fourier transform. By completion of this book, the reader will be armed to solve the Schrödinger equation for arbitrarily complex potentials, and for single and multi-electron systems.
The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques for 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 attacked. 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 last 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 book is suitable for two different levels in computational physics. The first part is 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 andseveral-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.
This advanced textbook provides an introduction to the basic methods of computational physics.
Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them. Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.