A Course in Theoretical Physics 1st Edition by John Shepherd ISBN 978-1118481424 1118481429

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Product details: 

ISBN 10: 1118481429

ISBN 13: 978-1118481424

Author:  P. John Shepherd

This book is a comprehensive account of five extended modules covering the key branches of twentieth-century theoretical physics, taught by the author over a period of three decades to students on bachelor and master university degree courses in both physics and theoretical physics.

The modules cover nonrelativistic quantum mechanics, thermal and statistical physics, many-body theory, classical field theory (including special relativity and electromagnetism), and, finally, relativistic quantum mechanics and gauge theories of quark and lepton interactions, all presented in a single, self-contained volume.

In a number of universities, much of the material covered (for example, on Einstein’s general theory of relativity, on the BCS theory of superconductivity, and on the Standard Model, including the theory underlying the prediction of the Higgs boson) is taught in postgraduate courses to beginning PhD students.

A distinctive feature of the book is that full, step-by-step mathematical proofs of all essential results are given, enabling a student who has completed a high-school mathematics course and the first year of a university physics degree course to understand and appreciate the derivations of very many of the most important results of twentieth-century theoretical physics.

Table of contents: 

Part I. Nonrelativistic Quantum Mechanics

1. Basic Concepts of Quantum Mechanics
    1.1 Probability Interpretation of the Wave Function
    1.2 States of Definite Energy and Momentum
    1.3 Observables and Operators
    1.4 Examples of Operators
    1.5 Time-Dependent Schrödinger Equation
    1.6 Stationary States and Time-Independent Schrödinger Equation
    1.7 Eigenvalue Spectra and Measurement Results
    1.8 Hermitian Operators
    1.9 Expectation Values of Observables
    1.10 Commuting Observables and Simultaneous Observability
    1.11 Noncommuting Observables and the Uncertainty Principle
    1.12 Time Dependence of Expectation Values
    1.13 Probability-Current Density
    1.14 General Form of Wave Functions
    1.15 Angular Momentum
    1.16 Particle in a 3D Spherically Symmetric Potential
    1.17 The Hydrogen-like Atom

2. Representation Theory
    2.1 Dirac Representation of States
    2.2 Completeness and Closure
    2.3 Changes of Representation
    2.4 Representation of Operators
    2.5 Hermitian Operators
    2.6 Products of Operators
    2.7 Formal Theory of Angular Momentum

3. Approximation Methods
    3.1 Time-Independent Perturbation Theory (Nondegenerate States)
    3.2 Time-Independent Perturbation Theory (Degenerate States)
    3.3 Variational Method
    3.4 Time-Dependent Perturbation Theory

4. Scattering Theory
    4.1 Evolution Operators and Møller Operators
    4.2 Scattering Operator and Scattering Matrix
    4.3 Green Operator and T Operator
    4.4 Stationary Scattering States
    4.5 Optical Theorem
    4.6 Born Series and Born Approximation
    4.7 Spherically Symmetric Potentials & Partial Waves
    4.8 Partial-Wave Scattering States

Part II. Thermal and Statistical Physics

5. Fundamentals of Thermodynamics
    (zeroth law, temperature, energy, heat, processes, first law, heat capacities, ideal gases, etc.)

6. Quantum States and Temperature

7. Microstate Probabilities and Entropy

8. The Ideal Monatomic Gas

9. Applications of Classical Thermodynamics

10. Thermodynamic Potentials and Derivatives

11. Matter Transfer and Phase Diagrams

12. Fermi–Dirac and Bose–Einstein Statistics

Part III. Many-Body Theory

13. Quantum Mechanics and Low-Temperature Thermodynamics of Many-Particle Systems

14. Second Quantization

15. Gas of Interacting Electrons

16. Superconductivity

Part IV. Classical Field Theory and Relativity

17. The Classical Theory of Fields

18. General Relativity

Part V. Relativistic Quantum Mechanics and Gauge Theories

19. Relativistic Quantum Mechanics

20. Gauge Theories of Quark and Lepton Interactions

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