Physics Formulary: Table of Contents

Last change: December 16, 2009

This document is a LaTeX file of 108 pages which contains a lot of equations in physics. It is written at advanced undergraduate/postgraduate level. It is intended to be a short reference for anyone who works with physics and often needs to look up equations.

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Equations in physics - Contents

The table of contents from "Equations in Physics" is shown below.

 Physical Constants 1
1. Mechanics 2
 1.1 Point-kinetics in a fixed coordinate system 2
 1.1.1 Definitions 2
 1.1.2 Polar coordinates 2
 1.2 Relative motion 2
 1.3 Point-dynamics in a fixed coordinate system 2
 1.3.1 Force, (angular)momentum and energy 2
 1.3.2 Conservative force fields 3
 1.3.3 Gravitation 3
 1.3.4 Orbital equations 3
 Kepler's equations 4
 1.3.5 The virial theorem 4
 1.4 Point dynamics in a moving coordinate system 4
 1.4.1 Apparent forces 4
 1.4.2 Tensor notation 5
 1.5 Dynamics of masspoint collections 5
 1.5.1 The centre of mass 5
 1.5.2 Collisions 6
 1.6 Dynamics of rigid bodies 6
 1.6.1 Moment of Inertia 6
 1.6.2 Principal axes 6
 1.6.3 Time dependence 6
 1.7 Variational Calculus, Hamilton and Lagrange mechanics 7
 1.7.1 Variational Calculus 7
 1.7.2 Hamilton mechanics 7
 1.7.3 Motion around an equilibrium, linearization 7
 1.7.4 Phase space, Liouville's equation 8
 1.7.5 Generating functions 8
2. Electricity & Magnetism 9
 2.1 The Maxwell equations 9
 2.2 Force and potential 9
 2.3 Gauge transformations 10
 2.4 Energy of the electromagnetic field 10
 2.5 Electromagnetic waves 10
 2.5.1 Electromagnetic waves in vacuum 10
 2.5.2 Electromagnetic waves in matter 11
 2.6 Multipoles 11
 2.7 Electric currents 11
 2.8 Depolarizing field 12
 2.9 Mixtures of materials 12
3. Relativity 13
 3.1 Special relativity 13
 3.1.1 The Lorentz transformation 13
 3.1.2 Red and blue shift 14
 3.1.3 The stress-energy tensor and the field tensor 14
 3.2 General relativity 14
 3.2.1 Riemannian geometry, the Einstein tensor 14
 3.2.2 The line element 15
 3.2.3 Planetary orbits and the perihelion shift 16
 3.2.4 The trajectory of a photon 17
 3.2.5 Gravitational waves 17
 3.2.6 Cosmology 17
4. Oscillations 18
 4.1 Harmonic oscillations 18
 4.2 Mechanic oscillations 18
 4.3 Electric oscillations 19
 4.4 Waves in long conductors 19
 4.5 Coupled conductors and transformers 19
 4.6 Pendulums 19
5. Waves 20
 5.1 The wave equation 20
 5.2 Solutions of the wave equation 20
 5.2.1 Plane waves 20
 5.2.2 Spherical waves 21
 5.2.3 Cylindrical waves 21
 5.2.4 The general solution in one dimension 21
 5.3 The stationary phase method 21
 5.4 Green functions for the initial-value problem 22
 5.5 Waveguides and resonating cavities 22
 5.6 Non-linear wave equations 23
6. Optics 24
 6.1 The bending of light 24
 6.2 Paraxial geometrical optics 24
 6.2.1 Lenses 24
 6.2.2 Mirrors 25
 6.2.3 Principal planes 25
 6.2.4 Magnification 25
 6.3 Matrix methods 25
 6.4 Aberrations 26
 6.5 Reflection and transmission 26
 6.6 Polarization 27
 6.7 Prisms and dispersion 27
 6.8 Diffraction 28
 6.9 Special optical effects 28
 6.10 The Fabry-Perot interferometer 29
7. Statistical physics 30
 7.1 Degrees of freedom 30
 7.2 The energy distribution function 30
 7.3 Pressure on a wall 31
 7.4 The equation of state 31
 7.5 Collisions between molecules 32
 7.6 Interaction between molecules 32
8. Thermodynamics 33
 8.1 Mathematical introduction 33
 8.2 Definitions 33
 8.3 Thermal heat capacity 33
 8.4 The laws of thermodynamics 34
 8.5 State functions and Maxwell relations 34
 8.6 Processes 35
 8.7 Maximal work 36
 8.8 Phase transitions 36
 8.9 Thermodynamic potential 37
 8.10 Ideal mixtures 37
 8.11 Conditions for equilibrium 37
 8.12 Statistical basis for thermodynamics 38
 8.13 Application to other systems 38
9. Transport phenomena 39
 9.1 Mathematical introduction 39
 9.2 Conservation laws 39
 9.3 Bernoulli's equations 41
 9.4 Characterising of flows with dimensionless numbers 41
 9.5 Tube flows 42
 9.6 Potential theory 42
 9.7 Boundary layers 43
 9.7.1 Flow boundary layers 43
 9.7.2 Temperature boundary layers 43
 9.8 Heat conductance 44
 9.9 Turbulence 44
 9.10 Self organization 44
10. Quantum physics 45
 10.1 Introduction to quantum physics 45
 10.1.1 Black body radiation 45
 10.1.2 The Compton effect 45
 10.1.3 Electron diffraction 45
 10.2 Wave functions 45
 10.3 Operators in quantum physics 45
 10.4 The uncertainty principle 46
 10.5 The Schr\"odinger equation 46
 10.6 Parity 46
 10.7 The tunnel effect 47
 10.8 The harmonic oscillator 47
 10.9 Angular momentum 47
 10.10 Spin 48
 10.11 The Dirac formalism 48
 10.12 Atomic physics 49
 10.12.1 Solutions 49
 10.12.2 Eigenvalue equations 49
 10.12.3 Spin-orbit interaction 49
 10.12.4 Selection rules 50
 10.13 Interaction with electromagnetic fields 50
 10.14 Perturbation theory 50
 10.14.1 Time-independent perturbation theory 50
 10.14.2 Time-dependent perturbation theory 51
 10.15 N-particle systems 51
 10.15.1 General 51
 10.15.2 Molecules 52
 10.16 Quantum statistics 52
11. Plasma physics 54
 11.1 Introduction 54
 11.2 Transport 54
 11.3 Elastic collisions 55
 11.3.1 General 55
 11.3.2 The Coulomb interaction 56
 11.3.3 The induced dipole interaction 56
 11.3.4 The centre of mass system 56
 11.3.5 Scattering of light 56
 11.4 Thermodynamic equilibrium and reversibility 57
 11.5 Inelastic collisions 57
 11.5.1 Types of collisions 57
 11.5.2 Cross sections 58
 11.6 Radiation 58
 11.7 The Boltzmann transport equation 59
 11.8 Collision-radiative models 60
 11.9 Waves in plasma's 60
12. Solid state physics 62
 12.1 Crystal structure 62
 12.2 Crystal binding 62
 12.3 Crystal vibrations 63
 12.3.1 A lattice with one kind of atoms 63
 12.3.2 A lattice with two kinds of atoms 63
 12.3.3 Phonons 63
 12.3.4 Thermal heat capacity 64
 12.4 Magnetic field in the solid state 65
 12.4.1 Dielectrics 65
 12.4.2 Paramagnetism 65
 12.4.3 Ferromagnetism 65
 12.5 Free electron Fermi gas 66
 12.5.1 Thermal heat capacity 66
 12.5.2 Electric conductance 66
 12.5.3 The Hall-effect 66
 12.5.4 Thermal heat conductivity 67
 12.6 Energy bands 67
 12.7 Semiconductors 67
 12.8 Superconductivity 68
 12.8.1 Description 68
 12.8.2 The Josephson effect 69
 12.8.3 Flux quantisation in a superconducting ring 69
 12.8.4 Macroscopic quantum interference 69
 12.8.5 The London equation 70
 12.8.6 The BCS model 70
13. Theory of groups 71
 13.1 Introduction 71
 13.1.1 Definition of a group 71
 13.1.2 The Cayley table 71
 13.1.3 Conjugated elements, subgroups and classes 71
 13.1.4 Isomorfism and homomorfism; representations 72
 13.1.5 Reducible and irreducible representations 72
 13.2 The fundamental orthogonality theorem 72
 13.2.1 Schur's lemma 72
 13.2.2 The fundamental orthogonality theorem 72
 13.2.3 Character 72
 13.3 The relation with quantum mechanics 73
 13.3.1 Representations, energy levels and degeneracy 73
 13.3.2 Breaking of degeneracy with a perturbation 73
 13.3.3 The construction of a basefunction 73
 13.3.4 The direct product of representations 74
 13.3.5 Clebsch-Gordan coefficients 74
 13.3.6 Symmetric transformations of operators,
 irreducible tensor operators 74
 13.3.7 The Wigner-Eckart theorem 75
 13.4 Continuous groups 75
 13.4.1 The 3-dimensional translation group 75
 13.4.2 The 3-dimensional rotation group 76
 13.4.3 Properties of continuous groups 76
 13.5 The group SO(3) 77
 13.6 Applications to quantum mechanics 78
 13.6.1 Vectormodel for the addition of angular momentum 78
 13.6.2 Irreducible tensoroperators, matrixelements and
 selection rules 78
 Some examples of the behaviour of operators
 under SO(3) 78
 Selection rules for dipole transitions 79
 Land\'e -equation for the anomalous
 Zeeman splitting 79
 13.7 Applications to particle physics 79
14. Nuclear physics 81
 14.1 Nuclear forces 81
 14.2 The shape of the nucleus 82
 14.3 Radioactive decay 82
 14.4 Scattering and nuclear reactions 83
 14.4.1 Kinetic model 83
 14.4.2 Quantum mechanical model for n-p scattering 83
 14.4.3 Conservation of energy and momentum in nuclear
 reactions 84
 14.5 Radiation dosimetry 84
15. Quantum field theory & Particle physics 85
 15.1 Creation and annihilation operators 85
 15.2 Classical and quantum fields 85
 15.3 The interaction picture 86
 15.4 Real scalar field in the interaction picture 86
 15.5 Charged spin-0 particles, conservation of charge 87
 15.6 Field functions for 1/2-particles 87
 15.7 Quantization of spin-1/2 fields 88
 15.8 Quantization of the electromagnetic field 89
 15.9 Interacting fields and the S-matrix 89
 15.10 Divergences and renormalization 90
 15.11 Classification of elementary particles 90
 15.12 P and CP-violation 92
 15.13 The standard model 93
 15.13.1 The electroweak theory 93
 15.13.2 Spontaneous symmetry breaking: the Higgs mechanism 94
 15.13.3 Quantumchromodynamics 94
 15.14 Pathintegrals 95
 15.15 Unification and quantum gravity 95
16. Astrophysics 96
 16.1 Determination of distances 96
 16.2 Brightness and magnitudes 96
 16.3 Radiation and stellar atmospheres 97
 16.4 Composition and evolution of stars 97
 16.5 Energy production in stars 98
The Nabla operator 99
The SI units 100