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Modern Physics
Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity, and general relativity. ''Classical physics'' is typically concerned with everyday conditions: speeds are much lower than the speed of light, sizes are much greater than that of atoms, and energies are relatively small. Modern physics, however, is concerned with more extreme conditions, such as high velocities that are comparable to the speed of light (special relativity), small distances comparable to the atomic radius (quantum mechanics), and very high energies (relativity). In general, quantum and relativistic effects are believed to exist across all scales, although these effects may be very small at human scale. While quantum mechanics is compatible with special relativity (See: Relativistic quantum mechanics), one of the unsolved problems ...
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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 ...
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Black-body Radiation
Black-body radiation is the thermal radiation, thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific continuous spectrum that depends only on the body's temperature., Chapter 13. A perfectly-insulated enclosure which is in thermal equilibrium internally contains blackbody radiation and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary objects can be approximated as blackbody radiation. Of particular importance, although planets and stars (including the Earth and Sun) are neither in thermal equilibrium with their surroundings nor perfect black bodies, blackbody radiation is still a good first approximation for the energy they emit. The term ''black body'' was introduced by Gustav Kirchhoff in 1860. ...
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Black Body
A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is called ''black-body radiation''. The name "black body" is given because it absorbs all colors of light. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions." A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition. An ideal black body in thermal equilibrium has two main properties: #It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature. ...
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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 ...
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Approximation Theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characterizing the approximation error, errors introduced thereby. What is meant by ''best'' and ''simpler'' will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or Rational function, rational (ratio of polynomials) approximations. The objective is to make the approxi ...
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Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist. Notation In formulas, a limit of a function is usually written as : \lim_ f(x) = L, and is read as "the limit of of as approaches equals ". This means that the value of the function can be made arbitrarily close to , by choosing sufficiently close to . Alternatively, the fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or ...
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Quantum
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ...
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Max Planck
Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of Quantum mechanics, quantum theory and one of the founders of modern physics, which revolutionized understanding of atomic and Subatomic particle, subatomic processes. He is known for the Planck constant, which is of foundational importance for quantum physics, and which he used to derive a set of Unit of measurement, units, today called Planck units, expressed only in terms of fundamental physical constants. Planck was twice president of the German scientific institution Kaiser Wilhelm Society. In 1948, it was renamed the Max Planck Society (Max-Planck-Gesellschaft) and nowadays includes 83 institutions representing a wide range ...
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Theory Of Relativity
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmolog ...
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Albert Einstein
Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula , which arises from special relativity, has been called "the world's most famous equation". He received the 1921 Nobel Prize in Physics for . Born in the German Empire, Einstein moved to Switzerland in 1895, forsaking his German citizenship (as a subject of the Kingdom of Württemberg) the following year. In 1897, at the age of seventeen, he enrolled in the mathematics and physics teaching diploma program at the Swiss ETH Zurich, federal polytechnic school in Zurich, graduating in 1900. He acquired Swiss citizenship a year later, which he kept for the rest of his life, and afterwards secured a permanent position at the Swiss Patent Office in Bern. In 1905, he submitted a successful PhD dissertation to the University of Zurich. In 19 ...
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Bose–Einstein Distribution
Bose–Einstein may refer to: * Bose–Einstein condensate, a phase of matter in quantum mechanics ** Bose–Einstein condensation (network theory), the application of this model in network theory ** Bose–Einstein condensation of polaritons ** Bose–Einstein condensation of quasiparticles * Bose–Einstein correlations * Bose–Einstein integral * Bose–Einstein statistics, in particle statistics See also *Bose (other) *Einstein (other) *Boson (other) *Satyendra Nath Bose Satyendra Nath Bose (; 1 January 1894 – 4 February 1974) was an Indian theoretical physicist and mathematician. He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose–Einstein statist ..., Indian physicist * Albert Einstein (other) {{disambiguation ...
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