Course in Theoretical Physics

Informationen zum Autor P. John Shepherd , Emeritus Professor, retired, formerly at the Department of Physics, University of Exeter, UK. Thirty years of teaching undergraduate physics. Klappentext 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. "The book is self-contained, and should be comprehensible to anyone who completed high-school mathematics." ("Book News", 1 June 2013) Zusammenfassung 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. Inhaltsverzeichnis Notation xiii Preface xv I Nonrelativistic Quantum Mechanics 1 1 Basic Concepts of Quantum Mechanics 3 1.1 Probability interpretation of the wave function 3 1.2 States of definite energy and states of definite momentum 4 1.3 Observables and operators 5 1.4 Examples of operators 5 1.5 The time-dependent Schrödinger equation 6 1.6 Stationary states and the time-independent Schrödinger equation 7 1.7 Eigenvalue spectra and the results of measurements 8 1.8 Hermitian operators 8 1.9 Expectation values of observables 10 1.10 Commuting observables and simultaneous observability 10 1.11 Noncommuting observables and the uncertainty principle 11 1.12 Time dependence of expectation values 12 1.13 The probability-current density 12 1.14 The general form of wave functions 12 1.15 Angular momentum 15 1.16 Particle in a three-dimensional spherically symmetric potential 17 1.17 The hydrogen-like atom 18 2 Representation Theory 23 2.1 Dirac representation of quantum mechanical states 23 2.2 Completeness and closure 27 2.3 Changes of representation 28 2.4 Representation of operators 29 2.5 Hermitian operators 31 2.6 Products of operators 31 2.7 Formal theory of angular momentum 32 3 Approximation Methods 39 3.1 Time-independent perturbation theory for nondegenerate states 39 3.2 Time-independent perturbation theory for degenerate states 44 3.3 The variational method 50 3.4 Time-dependent perturbation theory 54 4 Scattering Theory 63 4.1 Evolution operators and Møller operators 63 4.2 The scattering operator and scattering matrix 66 4.3 The Green operator and T operator 70 4.4 The stationary scattering states 76 4.5 The optical theorem 83 4.6 The Born ser...

List of contents

Notation xiii
 
Preface xv
 
I NONRELATIVISTIC QUANTUM MECHANICS 1
 
1 Basic Concepts of Quantum Mechanics 3
 
1.1 Probability interpretation of the wave function 3
 
1.2 States of definite energy and states of definite momentum 4
 
1.3 Observables and operators 5
 
1.4 Examples of operators 5
 
1.5 The time-dependent Schr¨odinger equation 6
 
1.6 Stationary states and the time-independent Schr¨odinger equation 7
 
1.7 Eigenvalue spectra and the results of measurements 8
 
1.8 Hermitian operators 8
 
1.9 Expectation values of observables 10
 
1.10 Commuting observables and simultaneous observability 10
 
1.11 Noncommuting observables and the uncertainty principle 11
 
1.12 Time dependence of expectation values 12
 
1.13 The probability-current density 12
 
1.14 The general form of wave functions 12
 
1.15 Angular momentum 15
 
1.16 Particle in a three-dimensional spherically symmetric potential 17
 
1.17 The hydrogen-like atom 18
 
2 Representation Theory 23
 
2.1 Dirac representation of quantum mechanical states 23
 
2.2 Completeness and closure 27
 
2.3 Changes of representation 28
 
2.4 Representation of operators 29
 
2.5 Hermitian operators 31
 
2.6 Products of operators 31
 
2.7 Formal theory of angular momentum 32
 
3 Approximation Methods 39
 
3.1 Time-independent perturbation theory for nondegenerate states 39
 
3.2 Time-independent perturbation theory for degenerate states 44
 
3.3 The variational method 50
 
3.4 Time-dependent perturbation theory 54
 
4 Scattering Theory 63
 
4.1 Evolution operators and Møller operators 63
 
4.2 The scattering operator and scattering matrix 66
 
4.3 The Green operator and T operator 70
 
4.4 The stationary scattering states 76
 
4.5 The optical theorem 83
 
4.6 The Born series and Born approximation 85
 
4.7 Spherically symmetric potentials and the method of partial waves 87
 
4.8 The partial-wave scattering states 92
 
II THERMAL AND STATISTICAL PHYSICS 97
 
5 Fundamentals of Thermodynamics 99
 
5.1 The nature of thermodynamics 99
 
5.2 Walls and constraints 99
 
5.3 Energy 100
 
5.4 Microstates 100
 
5.5 Thermodynamic observables and thermal fluctuations 100
 
5.6 Thermodynamic degrees of freedom 102
 
5.7 Thermal contact and thermal equilibrium 103
 
5.8 The zeroth law of thermodynamics 104
 
5.9 Temperature 104
 
5.10 The International Practical Temperature Scale 107
 
5.11 Equations of state 107
 
5.12 Isotherms 108
 
5.13 Processes 109
 
5.13.1 Nondissipative work 109
 
5.13.2 Dissipative work 111
 
5.13.3 Heat flow 112
 
5.14 Internal energy and heat 112
 
5.14.1 Joule's experiments and internal energy 112
 
5.14.2 Heat 113
 
5.15 Partial derivatives 115
 
5.16 Heat capacity and specific heat 116
 
5.16.1 Constant-volume heat capacity 117
 
5.16.2 Constant-pressure heat capacity 117
 
5.17 Applications of the first law to ideal gases 118
 
5.18 Difference of constant-pressure and constant-volume heat capacities 119
 
5.19 Nondissipative-compression/expansion adiabat of an ideal gas 120
 
6 Quantum States and Temperature 125
 
6.1 Quantum states 125
 
6.2 Effects of interactions 128
 
6.3 Statistical meaning of temperature 130
 
6.4 The Boltzmann distribution 134
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"The book is self-contained, and should be comprehensible to anyone who completed high-school mathematics." ( Book News , 1 June 2013)

Product details

• Authors: P John Shepherd, P. John Shepherd, Peter J. Shepherd, Pj Shepherd, SHEPHERD P JOHN, Shepherd P. John
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 22.02.2013
• EAN: 9781118481424
• ISBN: 978-1-118-48142-4
• No. of pages: 482
• Dimensions: 193 mm x 248 mm x 24 mm
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Physik, Theoretische Physik, Physics, Theoretical Physics