This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explantory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages --- Mathematica and Maple --- while some problems are implemented in C++. --
Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package.This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages — Mathematica and Maple — while some problems are implemented in C++.Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose-Fermi systems, super-Lie algebras, etc.
This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explantory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages --- Mathematica and Maple --- while some problems are implemented in C++. --
Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays the labor of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching tasks, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer.This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++.Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented.The level of presentation is such that one can get a sound grasp of computational techniques early on in one's scientific education. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.
This book revisits many of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding and visualizing analytical and numerical solutions. It subsequently uses these implementations as building blocks to solve more complex problems, such as coherent laser-driven dynamics in the Rubidium hyperfine structure or the Rashba interaction of an electron moving in 2D. The simulations are highlighted using the programming language Mathematica. No prior knowledge of Mathematica is needed; alternatives, such as Matlab, Python, or Maple, can also be used.
The book gives a thorough introduction into object orientated design and programming using C++. At the same time it can be used as a library of very useful programs chosen from the fields of finance, adminstration and statistics. These include programs for calculating loan periods, amortization, least squares fitting, a spelling checker, Gregorian calendar, data compression and encryption, searching and sorting. Basic C++ programming is introduced with simple introductory programs while object-oriented programming in C++ is explained as we develop useful classes. Finally we give an introduction into object orientated design and we demonstrate its power by developing a banking package.
The Companion Media Pack is available in the .Introduction to Windows® and Graphics Programming with Visual C++® (2nd Edition) provides an accessible approach to the study of Windows programming. It is intended to be an introduction to Visual C++ for technical people including practicing engineers, engineering students, and others interested in Windows programming and its convenient graphics capabilities. While the book is aimed at a technical audience, its mathematical content is modest and should be readable by most people with an interest in C++ programming. Readers are introduced to Windows programming in a natural way; making use of the object-oriented environment, the Microsoft Foundation Classes (MFC), and the document/view organization. Visual C++ is part of Microsoft's Visual Studio and provides full support of program development at all stages — from design to debugging.This second edition brings the original book up to date reflecting the evolution of Visual C++ and the Windows environment since the first edition. All example projects, figures and text in the book have been revised and coverage of touch screen developments has been added. Two new chapters on touch screen programming are based on programming strategies developed throughout the book. New examples demonstrate touch screen operations and consider programming for a tablet environment. More than seventy example projects are provided in the book's Companion Media Pack. The structure and coding for each example project are described thoroughly in a step-by-step fashion. Exercises at the end of each chapter provide opportunities to revisit and extend the tutorial examples. The media pack files include complete program code for all projects as well as files with classes and functions for handling geometric objects and graphs. The graphics examples require only standard Microsoft resources and may be easily adapted for a wide variety of application programs.The Companion Media Pack can be readily updated as Visual C++ continues to evolve. For example, the first update of the media pack was made after the release of a new version of Visual C++. It provides a full set of example projects developed with the new version as an addition to the book's original examples. Continuing updates of the media pack are planned as appropriate.
The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
