QUANTUM MECHANICS USING COMPUTER ALGEBRA
Includes Sample Programs in C++, SymbolicC++, Maxima, Maple, and Mathematica
(2nd Edition)
by Willi-Hans Steeb (University of Johannesburg, South Africa)
&
Yorick Hardy (University of Johannesburg, South Africa)
Table of Contents (88k)
Preface (47k)
Chapter 1: Introduction (117k)
Chapter 2: Conservation Law and Schrödinger Equation (42k)
Chapter 3: Wave Packet and Free Schrödinger Equation (38k)
Chapter 4: Separation Ansatz and Schrödinger Equation (36k)
Chapter 5: Matrix Representation in the Hilbert Space L2[-π,π] (44k)
Chapter 6: One-Dimensional Potential and Trial Function (36k)
Chapter 7: Heisenberg Equation of Motion (47k)
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.
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