Mathematical Physics

ISBN-13: 9783527408085 / Angielski / Miękka / 2010 / 466 str.

Shigeji Fujita; Salvador V. Godoy

Opis

This topical new book discusses in detail the mathematical skills needed throughout common graduate level courses in physics. It integrates the mathematics with the associated physical content, providing a new standard in mathematical physics textbooks and features approximately 450 end-of-chapter problems, with free solutions available to lecturers from the Wiley-VCH website.

Spis treści

1. Vectors
2. Tensors and Matrices
3. Hamiltonian Mechanics
4. Coupled Oscillators and Normal Modes
5. Stretched String
6. Vector Calculus and the del Operator
7. Electromagnetic Waves
8. Fluid Dynamics
9. Irreversible Processes
10. The Entropy
11. Thermodynamic Inequalities
12. Probability, Statistics and Density
13. Liouville Equation
14. Generalized Vectors and Linear Operators
15. Quantum Mechanics
16. Fourier Series and Transforms
17. Angular Momentum
18. Spin Angular Momentum
19. Time–dependent Perturbation Theory
20. Laplace Transformation
21. Quantum Harmonic Oscillator
22. Permutation Group
23. Quantum Statistics
24. The Free–Electron Model
25. Bose–Einstein Condensation
26. Magnetic Susceptibility
27. Theory of Variations
28. Second Quantization
29. Quantum Statistics of Composites
30. Superconductivity
31. Complex Numbers
32. Analyticity and Cauchy–Riemann Equations
33. Cauchy′s Fundamental Theorem
34. Laurent Series
35. Multivalued Functions
36. Residue Theorem and its Applications
Appendices
A. Representation–Independence of Poisson Brackets
B. Proof of the Convolution Theorem
C. Statistical Weight of the Landau States
D. Useful Formulas

O autorze

Shigeji Fujita was awarded his Ph.D. degree in physics from the University of Maryland at College Park in 1960. He subsequently worked as a research assistant and assistant professor at various Japanese and American universities and held visiting appointments at universities around the world. In 1968, he was appointed to a professorship at the Department of Physics of the State University of New York at Buffalo, which is where he still teaches. Professor Fujita conducts research in several areas, among others in equilibrium and non–equilibrium statistical mechanics, the Kinetic Theory of plasmas, gases, liquids and solids, and the Quantum Hall Effect. He has published over 200 articles and eleven books.

Salvador Godoy received his B.S. in physics from the National University of Mexico in 1967 and his Ph.D. from the State University of New York at Buffalo in 1973. In 1982 he was offered a full professorship at the Department of Physics, Facultad de Ciencias, at the Universidad Nacional Autónoma de México. Professor Godoy′s research interests lie in non–equilibrium statistical mechanics, mathematical physics, Laser theory and stochastic processes (among others). He has published about 60 papers and three books.

Blurb

Going beyond standard textbooks, this book presents mathematical topics with basic physics and also selected quantum physics topics with underlying mathematics.

Aimed at first–year graduate students, it is concise and discusses selected topics in full without omitting any steps. It covers the mathematical tools needed throughout common graduate level courses in physics and features around 450 end–of–chapter problems, with solutions available to lecturers from the Wiley website.

From the contents:

• Vectors
• Tensors and Matrices
• Hamiltonian Mechanics
• Coupled Oscillator and Normal Modes
• Stretched String
• Vector Calculus and the del Operator
• Electromagnetic Waves
• Fluid Dynamics
• Irreversible Processes
• The Entropy
• Thermodynamic Inequalities
• Probability, Statistics and Density
• Liouville Equation
• Generalized Vectors and Linear Operators
• Quantum Mechanics
• Fourier Series and Transforms
• Angular Momentum
• Spin Angular Momentum
• Time–dependent Perturbation Theory
• Laplace Transformation
• Quantum Harmonic Oscillator
• Permutation Group
• Quantum Statistics
• The Free–Electron Model
• Bose–Einstein Condensation
• Magnetic Susceptibility
• Theory of Variations
• Second Quantization
• Quantum Statistics of Composites
• Superconductivity
• Complex Numbers
• Analyticity and Cauchy–Reimann Equations
• Cauchy s Fundamental Theorem
• Laurent Series
• Multivalued Functions
• Residue Theorem and its Applications