Landau Rubin H. - Computational Physics

Paar, H.H.

An Introduction to Advanced Quantum Physics

2010

Print ISBN: 978-0-470-68675-1; also available in electronic formats

Har, J.J., Tamma, K.K.

Advances in Computational Dynamics of Particles, Materials and Structures

2012

Print ISBN: 978-0-470-74980-7; also available in electronic formats ISBN: 978-1-119-96589-3

Cohen-Tannoudji, C., Diu, B., Laloe, F.

Quantum Mechanics

2 Volume Set

1977

Print ISBN: 978-0-471-56952-7; also available in electronic formats

Schattke, W., Dez Muio, R.

Quantum Monte-Carlo Programming

for Atoms, Molecules, Clusters, and Solids

2013

Print ISBN: 978-3-527-40851-1; also available in electronic formats

Zelevinsky, V.

Quantum Physics 1&2

2 Volume Set

2011

Print ISBN: 978-3-527-41057-6; also available in electronic formats

3rd completely revised edition

Rubin H. Landau

Oregon State University
97331 Corvallis OR
United States

Manuel J. Pez
Universad de Antioquia
Departamento Fisica
Medellin
Colombia

Cristian C. Bordeianu

National Military College tefan cal Mare
Campulung Moldovenesc
Romania

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Print ISBN 978-3-527-41315-7

ePDF ISBN 978-3-527-68466-3

ePub ISBN 978-3-527-68469-4

Mobi ISBN 978-3-527-68467-0

To the memory of Jon Maestri

1. 1 Introduction
2. 2 Computing Software Basics
3. 3 Errors and Uncertainties in Computations
4. 4 Monte Carlo: Randomness, Walks, and Decays
5. 5 Differentiation and Integration
6. 6 Matrix Computing
7. 7 Trial-and-Error Searching and Data Fitting
8. 8 Solving Differential Equations: Nonlinear Oscillations
9. 9 ODE Applications: Eigenvalues, Scattering, and Projectiles
10. 10 High-Performance Hardware and Parallel Computers
11. 11 Applied HPC: Optimization, Tuning, and GPU Programming
12. 12 Fourier Analysis: Signals and Filters
13. 13 Wavelet and Principal Components Analyses: Nonstationary Signals and Data Compression
14. 14 Nonlinear Population Dynamics
15. 15 Continuous Nonlinear Dynamics
16. 16 Fractals and Statistical Growth Models
17. 17 Thermodynamic Simulations and Feynman Path Integrals
18. 18 Molecular Dynamics Simulations
19. 19 PDE Review and Electrostatics via Finite Differences and Electrostatics via Finite Differences
20. 20 Heat Flow via Time Stepping
21. 21 Wave Equations I: Strings and Membranes
22. 22 Wave Equations II: Quantum Packets and Electromagnetic
23. 23 Electrostatics via Finite Elements
24. 24 Shocks Waves and Solitons
25. 25 Fluid Dynamics
26. 26 Integral Equations of Quantum Mechanics

1. 1 Introduction
2. 2 Computing Software Basics
3. 3 Errors and Uncertainties in Computations
4. 4 Monte Carlo: Randomness, Walks, and Decays
5. 5 Differentiation and Integration
6. 6 Matrix Computing
7. 7 Trial-and-Error Searching and Data Fitting
8. 8 Solving Differential Equations: Nonlinear Oscillations
9. 10 High-Performance Hardware and Parallel Computers
10. 12 Fourier Analysis: Signals and Filters
11. 13 Wavelet and Principal Components Analyses: Nonstationary Signals and Data Compression
12. 18 Molecular Dynamics Simulations
13. 19 PDE Review and Electrostatics via Finite Differences and Electrostatics via Finite Differences
14. Appendix A: Codes, Applets, and Animations

Seventeen years have past since Wiley first published Landau and Pezs Computational Physics and twelve years since Cristian Bordeianu joined the collaboration for the second edition. This third edition adheres to the original philosophy that the best way to learn computational physics (CP) is by working on a wide range of projects using the text and the computer as partners. Most projects are still constructed using a computational, scientific problem-solving paradigm:

(0.1)

Our guiding hypothesis remains that CP is a computational science, which means that to understand CP you need to understand some physics, some applied mathematics, and some computer science. What is different in this edition is the choice of Python for sample codes and an increase in the number of topics covered. We now have a survey of CP which is more than enough for a full-years course.

The use of Python is more than just a change of language, it is taking advantage of the Python ecosystem of base language plus multiple, specialized libraries to provide all computational needs. In addition, we find Python to be the easiest and most accessible language for beginners, while still being excellent for the type of interactive and exploratory computations now popular in scientific research. Furthermore, Python supplemented by the Visual package (VPython) has gained traction in lower division physics teaching, and this may serve as an excellent segue to a Python-based CP course. Nevertheless, the important aspects of computational modeling and thinking transcends any particular computer language, and so having a Python alternative to our previous use of Fortran, C and Java may help promote this view (codes in all languages are available).

As before, we advocate for the use of a compiled or interpreted programming language when learning CP, in contrast to a higher level problem-solving environment like Mathematica or Maple, which we use in daily work. This follows from our experiences that if you want to understand how to compute scientifically, then you must look inside a programs black box and get your hands dirty. Otherwise, the algorithms, logic, and the validity of solutions cannot be ascertained, and that is not a good physics. Not surprisingly, we believe all physicists should know how to read programs how to write them as well.