Physics Formulary

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This document contains a 108 page \(\rm\LaTeX\) file which contains a lot 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.

This, and a Dutch version of this file, can be obtained from the author, Johan Wevers johanw@xs4all.nl.

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ir. J.C.A. Wevers

Contents

Physical Constants

  1. Mechanics
    1. Point-kinetics in a fixed coordinate system
      1. Definitions
      2. Polar coordinates
    2. Relative motion
    3. Point-dynamics in a fixed coordinate system
      1. Force, (angular)momentum and energy
      2. Conservative force fields
      3. Gravitation
      4. Orbital equations
        1. Kepler's equations
      5. The virial theorem
    4. Point dynamics in a moving coordinate system
      1. Apparent forces
      2. Tensor notation
    5. Dynamics of masspoint collections
      1. The centre of mass
      2. Collisions
    6. Dynamics of rigid bodies
      1. Moment of Inertia
      2. Principal axes
      3. Time dependence
    7. Variational Calculus, Hamilton and Lagrange mechanics
      1. Variational Calculus
      2. Hamilton mechanics
      3. Motion around an equilibrium, linearization
      4. Phase space, Liouville's equation
      5. Generating functions

  2. Electricity & Magnetism
    1. The Maxwell equations
    2. Force and potential
    3. Gauge transformations
    4. Energy of the electromagnetic field
    5. Electromagnetic waves
      1. Electromagnetic waves in vacuum
      2. Electromagnetic waves in matter
    6. Multipoles
    7. Electric currents
    8. Depolarizing field
    9. Mixtures of materials

  3. Relativity
    1. Special relativity
      1. The Lorentz transformation
      2. Red and blue shift
      3. The stress-energy tensor and the field tensor
    2. General relativity
      1. Riemannian geometry, the Einstein tensor
      2. The line element
      3. Planetary orbits and the perihelion shift
      4. The trajectory of a photon
      5. Gravitational waves
      6. Cosmology

  4. Oscillations
    1. Harmonic oscillations
    2. Mechanic oscillations
    3. Electric oscillations
    4. Waves in long conductors
    5. Coupled conductors and transformers
    6. Pendulums

  5. Waves
    1. The wave equation
    2. Solutions of the wave equation
      1. Plane waves
      2. Spherical waves
      3. Cylindrical waves
      4. The general solution in one dimension
    3. The stationary phase method
    4. Green functions for the initial-value problem
    5. Waveguides and resonating cavities
    6. Non-linear wave equations

  6. Optics
    1. The bending of light
    2. Paraxial geometrical optics
      1. Lenses
      2. Mirrors
      3. Principal planes
      4. Magnification
    3. Matrix methods
    4. Aberrations
    5. Reflection and transmission
    6. Polarization
    7. Prisms and dispersion
    8. Diffraction
    9. Special optical effects
    10. The Fabry-Perot interferometer

  7. Statistical physics
    1. Degrees of freedom
    2. The energy distribution function
    3. Pressure on a wall
    4. The equation of state
    5. Collisions between molecules
    6. Interaction between molecules

  8. Thermodynamics
    1. Mathematical introduction
    2. Definitions
    3. Thermal heat capacity
    4. The laws of thermodynamics
    5. State functions and Maxwell relations
    6. Processes
    7. Maximal work
    8. Phase transitions
    9. Thermodynamic potential
    10. Ideal mixtures
    11. Conditions for equilibrium
    12. Statistical basis for thermodynamics
    13. Application to other systems

  9. Transport phenomena
    1. Mathematical introduction
    2. Conservation laws
    3. Bernoulli's equations
    4. Characterising of flows with dimensionless numbers
    5. Tube flows
    6. Potential theory
    7. Boundary layers
      1. Flow boundary layers
      2. Temperature boundary layers
    8. Heat conductance
    9. Turbulence
    10. Self organization

  10. Quantum physics
    1. Introduction to quantum physics
      1. Black body radiation
      2. The Compton effect
      3. Electron diffraction
    2. Wave functions
    3. Operators in quantum physics
    4. The uncertainty principle
    5. The Schrödinger equation
    6. Parity
    7. The tunnel effect
    8. The harmonic oscillator
    9. Angular momentum
    10. Spin
    11. The Dirac formalism
    12. Atomic physics
      1. Solutions
      2. Eigenvalue equations
      3. Spin-orbit interaction
      4. Selection rules
    13. Interaction with electromagnetic fields
    14. Perturbation theory
      1. Time-independent perturbation theory
      2. Time-dependent perturbation theory
    15. N-particle systems
      1. General
      2. Molecules
    16. Quantum statistics

  11. Plasma physics
    1. Introduction
    2. Transport
    3. Elastic collisions
      1. General
      2. The Coulomb interaction
      3. The induced dipole interaction
      4. The centre of mass system
      5. Scattering of light
    4. Thermodynamic equilibrium and reversibility
    5. Inelastic collisions
      1. Types of collisions
      2. Cross sections
    6. Radiation
    7. The Boltzmann transport equation
    8. Collision-radiative models
    9. Waves in plasma's

  12. Solid state physics
    1. Crystal structure
    2. Crystal binding
    3. Crystal vibrations
      1. A lattice with one kind of atoms
      2. A lattice with two kinds of atoms
      3. Phonons
      4. Thermal heat capacity
    4. Magnetic field in the solid state
      1. Dielectrics
      2. Paramagnetism
      3. Ferromagnetism
    5. Free electron Fermi gas
      1. Thermal heat capacity
      2. Electric conductance
      3. The Hall-effect
      4. Thermal heat conductivity
    6. Energy bands
    7. Semiconductors
    8. Superconductivity
      1. Description
      2. The Josephson effect
      3. Flux quantisation in a superconducting ring
      4. Macroscopic quantum interference
      5. The London equation
      6. The BCS model

  13. Theory of groups
    1. Introduction
      1. Definition of a group
      2. The Cayley table
      3. Conjugated elements, subgroups and classes
      4. Isomorfism and homomorfism; representations
      5. Reducible and irreducible representations
    2. The fundamental orthogonality theorem
      1. Schur's lemma
      2. The fundamental orthogonality theorem
      3. Character
    3. The relation with quantum mechanics
      1. Representations, energy levels and degeneracy
      2. Breaking of degeneracy with a perturbation
      3. The construction of a basefunction
      4. The direct product of representations
      5. Clebsch-Gordan coefficients
      6. Symmetric transformations of operators, irreducible tensor operators
      7. The Wigner-Eckart theorem
    4. Continuous groups
      1. The 3-dimensional translation group
      2. The 3-dimensional rotation group
      3. Properties of continuous groups
    5. The group SO(3)
    6. Applications to quantum mechanics
      1. Vectormodel for the addition of angular momentum
      2. Irreducible tensoroperators, matrixelements and selection rules
        1. Some examples of the behaviour of operators under SO(3)
        2. Selection rules for dipole transitions
        3. Landé-equation for the anomalous Zeeman splitting
    7. Applications to particle physics

  14. Nuclear physics
    1. Nuclear forces
    2. The shape of the nucleus
    3. Radioactive decay
    4. Scattering and nuclear reactions
      1. Kinetic model
      2. Quantum mechanical model for n-p scattering
      3. Conservation of energy and momentum in nuclear reactions
    5. Radiation dosimetry

  15. Quantum field theory & Particle physics
    1. Creation and annihilation operators
    2. Vlassical and quantum fields
    3. The interaction picture
    4. Real scalar field in the interaction picture
    5. Charged spin-0 particles, conservation of charge
    6. Field functions for 1/2-particles
    7. Quantization of spin-1/2 fields
    8. Quantization of the electromagnetic field
    9. Interacting fields and the S-matrix
    10. Divergences and renormalization
    11. Classification of elementary particles
    12. P and CP-violation
    13. The standard model
      1. The electroweak theory
      2. Spontaneous symmetry breaking: the Higgs mechanism
      3. Quantumchromodynamics
    14. Path integrals
    15. Unification and quantum gravity

  16. Astrophysics
    1. Determination of distances
    2. Brightness and magnitudes
    3. Radiation and stellar atmospheres
    4. Composition and evolution of stars
    5. Energy production in stars

The Nabla operator

The SI units