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Computational Methods in Physics, Chemistry and Biology: An Introduction / Edition 1
     

Computational Methods in Physics, Chemistry and Biology: An Introduction / Edition 1

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by Paul Harrison
 

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ISBN-10: 047149562X

ISBN-13: 9780471495628

Pub. Date: 11/28/2001

Publisher: Wiley

Computational Methods in Physics, Chemistry ahd Biology offers an accessible introducton to key computational techniques used within science, including quantum mechanics, dynamics, evolutionary methods and molecular dynamics. Assuming only a limited background in computational methods, this book provides the reader with a series of comprehensive examples, problems

Overview

Computational Methods in Physics, Chemistry ahd Biology offers an accessible introducton to key computational techniques used within science, including quantum mechanics, dynamics, evolutionary methods and molecular dynamics. Assuming only a limited background in computational methods, this book provides the reader with a series of comprehensive examples, problems and practical-based tasks from the basics through to more complex ideas and techniques.

Beginning with an introduction to a numerical solution of Schr? dinger's Equation the text moves on to discuss pertubation theory, variational calculations, diffusion, dynamics, Monte Carlo simulations and genetic algorithms. Aimed at those new to the field, the book will enable the reader to develop and implement computational methods for the solutions of a range of problems in science.

Features:
* An accessible introduction covering a range of essential techniques applicable to key problems
* Numerous examples, problems and practical-based exercises.
* A supplementary website including solutions
This is essential reading for undergraudates taking courses in computational physics, or numerical methods. Also useful to students studying engineering, applied mathematics, computational chemistry and mathematical biology.

Product Details

ISBN-13:
9780471495628
Publisher:
Wiley
Publication date:
11/28/2001
Pages:
222
Product dimensions:
7.68(w) x 9.88(h) x 0.69(d)

Table of Contents

Prefacexi
Acknowledgementsxiii
About the authorxv
About the bookxvii
Introductionxix
1Numerical Solutions to Schrodinger's Equation1
1.1Particles and Classical Mechanics1
1.2Waves and Quantum Mechanics6
1.3Analytical Solutions to Schrodinger's Equation11
1.4The Shooting Method16
1.5Initial Conditions19
1.6Computational Implementation20
1.7Application to Parabolic Potentials22
1.8Improved Energy Eigenvalues25
1.9Further Convergence Tests: Pushing Accuracy to its Limits28
1.10Deduction of the Wave Functions31
1.11Three-Dimensional Potentials33
1.12Application to the Hydrogen Atom34
2Approximate Methods45
2.1Small Changes45
2.2Non-Degenerate Perturbation Theory46
2.3Computing the First-Order Correction48
2.4Computing the Second-Order Correction52
2.5Two-Dimensional Perturbing Potentials55
2.6The Variational Method58
2.7Application to the Hydrogen Atom60
2.8Application to Biased Quantum Wells64
3Matrix Methods71
3.1Basis sets71
3.2Expansion74
3.3Formation of the Matrix Equation76
3.4Solution of the Matrix Equation77
3.5Computational Implementation for Quantum Wells78
3.6Convergence Tests: Application to Parabolic Potentials82
3.7Solution of Schrodinger's Equation in Several Dimensions84
3.8Degenerate Perturbation Theory86
4Deterministic Simulations91
4.1Complex Time Dependent Systems91
4.2Classical Mechanics and Space Rockets92
4.3Simulation of Launch Trajectory96
4.4Verification of Computational Parameters98
4.5Fun with Simulations100
4.6Introduction to Diffusion101
4.7Theory104
4.8Boundary Conditions105
4.9Numerical Implementation105
4.10Convergence Tests107
4.11Constant Diffusion Coefficients and Universality108
4.12Non-linear Diffusion109
5Stochastic Simulations115
5.1Stochastic or Monte Carlo Simulations115
5.2Random Numbers116
5.3How Random is Random?117
5.4Monte Carlo Simulations of Electron Scattering118
5.5Tests and Limits121
5.6Simulations of Three-Level Systems123
5.7Changing Probabilities and Pauli Exclusion125
6Percolation Theory131
6.1Complex Many-Body Interacting Systems131
6.2Disease Propagation132
6.3Computational Implementation133
6.4The Dependence of Infection upon Immunisation137
6.5The Limit of Large Populations and Critical Densities140
6.6Mixed Magnetic Phases142
7Evolutionary Methods149
7.1Genetic Algorithms149
7.2The Fitness Function150
7.3Random (Monte Carlo) Generation of Genomes150
7.4Reproduction and Natural Selection156
7.5Implementation of a Genetic Algorithm160
7.6Mutation and Conclusion164
8Molecular Dynamics169
8.1Modelling Molecules and Crystals169
8.2Atom-Atom Interactions and Interaction Potentials170
8.3Simulations of Atomic Ensembles173
8.4Computational Implementation175
8.5Initial Simulations and Convergence Tests179
8.6Larger Ensembles and Reproducing Nature180
8.7Non-spherical Interaction Potentials182
8.8Organic Molecules183
Appendix AFortran implementation of the shooting method189
Appendix B[down triangle, open superscript 2] in spherical polar coordinates191
Appendix CA comment on the computer sourcecodes193
Appendix DNote for tutors195
References197
Index199

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