Modern Physics With Modern Computational Methods

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

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.

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.

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.

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts neces

The first half of this book is designed as a course for first year graduate students in the sciences. Problems are chosen to illustrate mathematical and physical subjects. In this first half only a moderate background in physics and mathematics is assumed. Integration, Monte Carlo techniques, the solution of linear systems and finite element methods are treated with enough depth to allow the student to understand them. An introduction to modeling with differential methods, digital signal processing and chaos is given. One chapter provides an introduction to common computer architectures.In the second half a thorough understanding of quantum mechanics is assumed with the Schrvdinger equation being treated with scattering and bound state conditions. The time-dependent Schrvdinger equation is also solved. A thorough introduction to the solution of the quantum-mechanical bound state with variational and Monte Carlo Green's function is given, with two examples being the solution of the bound state nuclear helium 4 and the energy of atomic liquid helium 4 at zero temperature. The exact solution of the low energy scattering problem is presented. Algorithms for the Borel and Pade methods for the summation of divergent series are studied. In the final chapter, methods for the solution of hadronic scattering from nuclei are treated including single, double and multiple scattering as well as the derivation and calculation of multiple scattering through fundamental optical models.The first half of the book will be suitable for a general course in computational methods while the second half can serve as a second semester course for Physics majors intending to do work in hadronic physics orscattering.

This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.

A mathematical and computational education for students, researchers, and practising engineers.

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.

This advanced textbook provides an introduction to the basic methods of computational physics.