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Heisenberg Picture
In physics, the Heisenberg picture or Heisenberg representation is a Dynamical pictures, formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which observables incorporate a dependency on time, but the quantum state, states are time-independent. It stands in contrast to the Schrödinger picture in which observables are constant and the states evolve in time. It further serves to define a third, hybrid, picture, the interaction picture. Mathematical details In the Heisenberg picture of quantum mechanics the state vectors do not change with time, while observables satisfy where "H" and "S" label observables in Heisenberg and Schrödinger picture respectively, is the Hamiltonian (quantum mechanics), Hamiltonian and denotes the commutator of two operators (in this case and ). Taking expectation values automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem, the Heisenberg picture and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Physics
Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to post-1900 physics, which incorporates elements of quantum mechanics and the theory of relativity. However, relativity is based on classical field theory rather than quantum field theory, and is often categorized as a part of "classical physics". Overview ''Classical theory'' has at least two distinct meanings in physics. It can include all those areas of physics that do not make use of quantum mechanics, which includes classical mechanics (using any of the Newtonian, Lagrangian, or Hamiltonian formulations), as well as classical electrodynamics and relativity. Alternatively, the term can refer to theories that are neither quantum or relativistic. Depending on point of view, among the branches of theory sometimes included in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moyal Bracket
In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product. The Moyal bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a lengthy dispute with Paul Dirac. In the meantime this idea was independently introduced in 1946 by Hip Groenewold. Overview The Moyal bracket is a way of describing the commutator of observables in the phase space formulation of quantum mechanics when these observables are described as functions on phase space. It relies on schemes for identifying functions on phase space with quantum observables, the most famous of these schemes being the Wigner–Weyl transform. It underlies Moyal’s dynamical equation, an equivalent formulation of Heisenberg’s quantum equation of motion, thereby providing the quantum generalization of Hamilton’s equations. Mathematically, it is a deformation of the phase-space Poisson bracket (essential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior. Quantum theory A heuristic postulate called the correspondence principle was introduced to quantum theory by Niels Bohr: in effect it states that some kind of continuity argument should apply to the classical limit of quantum systems as the value of the Planck constant normalized by the action of these systems becomes very small. Often, this is approached through "quasi-classical" techniques (cf. WKB approximation). More rigorously, the mathematical operation involved in classical limits is a group contraction, approximating physical systems where the relevant action is much larger than the reduced Planck constant , so the "deformation parameter" / can be effectively taken to be zero (cf. Weyl quantization.) Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics involved Scientific Revolution, substantial change in the methods and philosophy of physics. The qualifier ''classical'' distinguishes this type of mechanics from physics developed after the History of physics#20th century: birth of modern physics, revolutions in physics of the early 20th century, all of which revealed limitations in classical mechanics. The earliest formulation of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton, and the mathematical methods invented by Newton, Gottfried Wilhelm Leibniz, Leonhard Euler and others to describe the motion of Physical body, bodies under the influence of forces. Later, methods bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCH Formula
BCH or BCh may refer to: Science and technology * BCH code (Bose–Chaudhuri–Hocquenghem code), a code in coding theory * Bachelor of Surgery, a component of some undergraduate medical degrees * Baker–Campbell–Hausdorff formula, in mathematics and Lie group theory * Biosafety Clearing-House, an international mechanism that exchanges information about the movement of genetically modified organisms * Birdsell Clover Huller, an agricultural machine * Bitcoin Cash, a peer-to-peer electronic cash system * Bean chitinase, a defensive enzyme Organisations * Birmingham Children's Hospital, a hospital in England * Boston Children’s Hospital, a hospital in Boston, Massachusetts * Blue Castle Holdings, developer of nuclear power stations in the US * British and Commonwealth Holdings, a defunct UK financial services company * Bataliony Chłopskie, a Polish resistance movement in World War II * Belfast City Hospital, a hospital in Northern Ireland * Central Bank of Honduras ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Rule
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as (u \cdot v)' = u ' \cdot v + u \cdot v' or in Leibniz's notation as \frac (u\cdot v) = \frac \cdot v + u \cdot \frac. The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts. Discovery Discovery of this rule is credited to Gottfried Leibniz, who demonstrated it using "infinitesimals" (a precursor to the modern differential). (However, J. M. Child, a translator of Leibniz's papers, argues that it is due to Isaac Barrow.) Here is Leibniz's argument: Let ''u'' and ''v'' be functions. Then ''d(uv)'' is the same thing as the difference between two successive ''uvs; let one of these be ''uv'', and the other ''u+du'' times ''v+dv''; then: \begin d(u\cdot v) & = (u + d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as \mathbb or . Histo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Operator
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a linear endomorphism. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermitian
{{Short description, none Numerous things are named after the French mathematician Charles Hermite (1822–1901): Hermite * Cubic Hermite spline, a type of third-degree spline * Gauss–Hermite quadrature, an extension of Gaussian quadrature method * Hermite class * Hermite differential equation * Hermite distribution, a parametrized family of discrete probability distributions * Hermite–Lindemann theorem, theorem about transcendental numbers * Hermite constant, a constant related to the geometry of certain lattices * Hermite-Gaussian modes * The Hermite–Hadamard inequality on convex functions and their integrals * Hermite interpolation, a method of interpolating data points by a polynomial * Hermite–Kronecker–Brioschi characterization * The Hermite–Minkowski theorem, stating that only finitely many number fields have small discriminants * Hermite normal form, a form of row-reduced matrices * Hermite numbers, integers related to the Hermite polynomials * Her ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Planck Constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum. The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Planck later referred to the constant as the "quantum of action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave itself. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". In metrology, the Planck constant is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-evolution Operator
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called ''stateful systems''). In this formulation, ''time'' is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies is governed by the principles of classical mechanics. In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by Newton's laws of motion. These principles can be equivalently expressed more abstractly by Hamiltonian mechanics or Lagrangian mechanics. The concept of time evolution may be applicable to other stateful systems as well. For instance, the operation of a Turing machine can be regarded as the time evolution of the machine's control state together with the state of the tape (or possibly multiple tapes) including the position of the machine's read-write head (or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
