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Quantization Of The Electromagnetic Field
The quantization of the electromagnetic field is a procedure in physics turning Maxwell's classical electromagnetic waves into particles called photons. Photons are massless particles of definite energy, definite momentum, and definite spin. To explain the photoelectric effect, Albert Einstein assumed heuristically in 1905 that an electromagnetic field consists of particles of energy of amount ''hν'', where ''h'' is the Planck constant and ''ν'' is the wave frequency. In 1927 Paul A. M. Dirac was able to weave the photon concept into the fabric of the new quantum mechanics and to describe the interaction of photons with matter. He applied a technique which is now generally called second quantization,The name derives from the second quantization of quantum mechanical wave functions. Such a wave function is a scalar field (the "Schrödinger field") and can be quantized in the very same way as electromagnetic fields. Since a wave function is derived from a "first" quantized Hamilt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Wave
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ranging from radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All forms of EMR travel at the speed of light in a vacuum and exhibit wave–particle duality, behaving both as waves and as discrete particles called photons. Electromagnetic radiation is produced by accelerating charged particles such as from the Sun and other celestial bodies or artificially generated for various applications. Its interaction with matter depends on wavelength, influencing its uses in communication, medicine, industry, and scientific research. Radio waves enable broadcasting and wireless communication, infrared is used in thermal imaging, visible light is essential for vision, and higher-energy radiation, such as X ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Potential
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a ''scalar potential'', which is a scalar field whose gradient is a given vector field. Formally, given a vector field \mathbf, a ''vector potential'' is a C^2 vector field \mathbf such that \mathbf = \nabla \times \mathbf. Consequence If a vector field \mathbf admits a vector potential \mathbf, then from the equality \nabla \cdot (\nabla \times \mathbf) = 0 (divergence of the curl is zero) one obtains \nabla \cdot \mathbf = \nabla \cdot (\nabla \times \mathbf) = 0, which implies that \mathbf must be a solenoidal vector field. Theorem Let \mathbf : \R^3 \to \R^3 be a solenoidal vector field which is twice continuously differentiable. Assume that \mathbf(\mathbf) decreases at least as fast as 1/\, \mathbf\, for \, \mathbf\, \to \infty . Define \mathbf (\mathbf) = \frac \int_ \frac \, d^3\mathbf where \nabla_y \times denotes curl with respect to variab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Expansion
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always Convergent series, converge. Well-behaved functions, for example Smoothness, smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transverse Field
Transverse may refer to: *Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle *Transverse flute, a flute that is held horizontally * Transverse force (or ''Euler force''), the tangential force that is felt in reaction to any angular acceleration *Transverse mass, a particle physics quantity *Transverse plane, the plane orthogonal to the anteroposterior or oral-aboral axis *Transverse rotors, a type of rotorcraft in which there are two rotors mounted side by side *Transverse wave, a wave that causes a disturbance in the medium perpendicular to the direction it advances *Transverse Island, an island on the east side of Stefansson Bay, off the coast of Enderby Land * ''Transverse'' (album), a 2012 album by Carter Tutti Void See also *Transversal (other) Transversal may refer to: * Transversal (combinatorics), a set containing exactly one member of each of several other sets * Transversal (geometry), a line th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb Gauge
In the physics of gauge theory, gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant Degrees of freedom (physics and chemistry), degrees of freedom in field (physics), field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a certain transformation, equivalent to a symmetry transformation, shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curl (mathematics)
In vector calculus, the curl, also known as rotor, is a vector operator that describes the Differential (infinitesimal), infinitesimal Circulation (physics), circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector (geometry), vector whose length and direction denote the Magnitude (mathematics), magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field. A vector field whose curl is zero is called irrotational. The curl is a form of derivative, differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Kelvin–Stokes theorem, Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve. The notation is more common in North America. In the rest of the world, particularly in 20th century scientific li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point. The elements of differential and integral calculus extend naturally to vector fields. When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus. Vector fields can usefully be thought of as representing the velocit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function (mathematics), function assigning a Euclidean vector, vector to each point of space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field
An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) describes their capacity to exert attractive or repulsive forces on another charged object. Charged particles exert attractive forces on each other when the sign of their charges are opposite, one being positive while the other is negative, and repel each other when the signs of the charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. These forces are described by Coulomb's law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Informally, the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annihilation Operator
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the creation operator i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creation Operator
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the creation operator is interpr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermions
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons. In contrast, particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin-statistics relation is, in fact, a spin statistics-quantum number relation. As ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
