PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Electrodynamics → Radiation and scattering ↓


Compton scattering


Compton scattering is a fundamental phenomenon in the field of radiation and scattering in electrodynamics. It helps us understand the dual nature of electromagnetic radiation, which shows both particle-like and wave-like properties. This effect, discovered by Arthur H. Compton in 1923, became a key piece of evidence supporting the quantum theory of light.

Understanding the basics

Compton scattering occurs when high-energy photons, such as X-rays or gamma rays, collide with free or loosely bound electrons of a target material. This interaction results in the scattering of the incoming photon and the transfer of energy to the electron, causing the electron to be ejected from the atom.

Compton effect

The Compton effect, named after Arthur Compton, who first observed it, is a change in the wavelength of the scattered photon. It shows that light has momentum and interacts with matter in particle-like ways, which is consistent with the quantum theory of light.

Photon–electron interaction

During this time, a photon with a specific frequency and wavelength hits an electron. The photon transfers part of its energy to the electron, which gains kinetic energy and momentum.

The main equation

The physics of Compton scattering is contained in the Compton wavelength displacement formula:

    Δλ = λ' - λ = (h / (m_e * c)) * (1 - cos(θ))

Where:

  • Δλ is the change in the wavelength of the photon.
  • λ' is the wavelength of the scattered photon.
  • λ is the initial wavelength of the photon.
  • h is the Planck constant (6.626 × 10^-34 Js).
  • m_e is the rest mass of the electron (9.109 × 10^-31 kg).
  • c is the speed of light in a vacuum (3 × 10^8 m/s).
  • θ is the scattering angle of the photon.

The energy of the photon before and after the collision can also be described using the energy-momentum conservation equations:

    E = h * ν

where E is the energy of the photon, h is the Planck constant, and ν is the frequency of the photon.

Visualization of Compton scattering

The simplest way to represent Compton scattering is through the interaction diagram:

Incoming photon Scattered photon ejected electron

In this diagram, the photon enters from the left, interacts with the electron, and then scatters. The incoming photon is depicted as a black line, the scattered photon as a blue line, and the ejected electron as a green line to highlight the transfer of energy and momentum.

Applications of Compton scattering

Compton scattering has a wide range of applications in both scientific research and practical technologies:

  • Medical imaging: Techniques such as CT scans and PET scans rely on understanding Compton scattering to create detailed images of the inside of the body.
  • Astronomy: Compton scattering is used to identify the properties of cosmic X-rays, helping astronomers detect celestial phenomena.
  • Materials analysis: Compton scattering is used in determining the electronic properties and chemical composition of materials.

Real life examples and simple analogy

To better understand Compton scattering, imagine a game of billiards. In this analogy, the cue ball represents the incoming photon, the target ball represents the electron, and the collision causes both balls (the photon and the electron) to move and change direction.

Example calculation

Let us consider an X-ray photon with an initial wavelength of 0.03 nm that collides with a stationary electron (θ = 90°). Calculate the change in wavelength.

    h = 6.626 × 10^-34 Js
m_e = 9.109 × 10^-31 kg
c = 3 × 10^8 m/s
θ = 90 degrees = π/2 radians
Δλ = (h / (m_e * c)) * (1 - cos(θ)) = (6.626 × 10^-34 / (9.109 × 10^-31 * 3 × 10^8)) * (1 - cos(π/2)) = 2.43 × 10^-12 m

The calculated change in wavelength is about 0.00243 nm.

Summary

Compton scattering highlights the complex nature of light and its interaction with matter. It provides insight into the quantum world, showing how conservation principles apply at the subatomic level. Understanding the Compton effect enables us to delve deeper into fields such as medical imaging, astronomy, and material science.


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Compton scattering

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