Category: Index

  • Einstein Field Equations

    Introduction The Einstein field equations (EFE) are the cornerstone of Einstein’s theory of general relativity. They describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. They were first published by Einstein in 1915. The Equation The Einstein field equations can be written as: Here is the Einstein…

  • Doppler Effect

    Introduction The Doppler Effect is a change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842. Basic Formulas The Doppler Effect can be described by the following formulas. For waves,…

  • Dispersion Relation

    Introduction A dispersion relation describes how the phase speed or group speed of a wave depends on its wavelength, or equivalently, how the energy of a particle depends on its momentum. The term “dispersion” refers to the phenomenon where the speed of a wave depends on its frequency. Basic Form of the Dispersion Relation In…

  • Dirac Equation

    Introduction The Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. It provides a description of elementary spin-1/2 particles, such as electrons, consistent with both quantum mechanics and the theory of special relativity. The Equation The Dirac equation in natural units () is written as: where is the wave…

  • Diffraction

    Introduction Diffraction is a wave phenomenon that occurs when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. It is characterized by the bending and spreading out of waves past the obstacle or through the slit. The Principle of Diffraction Diffraction is a result of the wave nature…

  • Decay Chains

    Introduction A decay chain, also known as a radioactive decay series or a radioactive cascade, is a sequence of radioactive decays of different radioactive isotopes, each decaying into a “daughter” isotope, which then decays into another, and so on until a stable isotope is reached. Types of Decay Three primary types of decay can occur…

  • Gamma Decay

    Introduction Gamma decay is a type of radioactive decay where an excited nucleus emits a gamma ray to reach a lower energy state. Unlike alpha and beta decay, gamma decay does not change the number of protons or neutrons in the nucleus, thus, the parent and daughter isotopes are the same. Gamma Rays Gamma rays…

  • Dielectric Materials

    Introduction Dielectric materials, or simply dielectrics, are insulators that can be polarized by an applied electric field. They do not conduct electricity but support electrostatic fields while dissipating minimal energy as heat. Properties Dielectrics are characterized by their dielectric constant, a measure of a material’s ability to store electrical energy in an electric field. The…

  • Davisson-Germer Experiment

    Introduction The Davisson-Germer experiment, conducted by Clinton Davisson and Lester Germer in 1927, confirmed the wave nature of electrons. The experiment provided key evidence supporting the de Broglie hypothesis, which proposed that particles can exhibit both particle-like and wave-like properties. The Experiment Davisson and Germer aimed an electron beam at a crystalline nickel target and…

  • Current Density

    Introduction Current density is a measure of the amount of electric current that flows through a particular cross-sectional area of a material per unit time. It is a fundamental concept in electromagnetism and is particularly important in the fields of electronics and materials science. Definition The current density is defined as the electric current per…