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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)
220pp
978-981-4307-16-1: US$55 / £36 US$41.25
/ £27
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.
Contents:
- Wave Packet and Free Schrodinger Equation
- Unitary Operators
- Unitary and Hermitian Operators
- Anharmonic Oscillator
- Radial Symmetric Potential and Bound States
- Helium Atom and Trial Function
- Gauge Theory
- Berry Phase
- Bose Operators and Number States
- Coherent States
- Perturbation Theory
- Teleportation
- Legendre Polynomials
- Hermite Polynomials
- Spherical Harmonics
- and other papers
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