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Quantum Theoretical Re-interpretation Of Kinematic And Mechanical Relations
In the history of physics, "On the quantum-theoretical reinterpretation of kinematical and mechanical relationships" (), also known as the ''Umdeutung'' (reinterpretation) paper, was a breakthrough article in quantum mechanics written by Werner Heisenberg, which appeared in ''Zeitschrift für Physik'' in September 1925. In the article, Heisenberg tried to explain the energy levels of a one-dimensional anharmonic oscillator, avoiding the concrete but unobservable representations of electron orbits by using observable parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states. Mathematically, Heisenberg showed the need of non-commutative operators. This insight would later become the basis for Heisenberg's uncertainty principle. This article was followed by the paper by Pascual Jordan and Max Born of the same year, and by the 'three-man paper' () by Born, Heisenberg and Jordan in 1926. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Physics
Physics is a branch of science whose primary objects of study are matter and energy. Discoveries of physics find applications throughout the natural sciences and in technology. Physics today may be divided loosely into classical physics and modern physics. Ancient history Elements of what became physics were drawn primarily from the fields of astronomy, optics, and mechanics, which were methodologically united through the study of geometry. These mathematical disciplines began in antiquity with the Babylonians and with Hellenistic writers such as Archimedes and Ptolemy. Ancient philosophy, meanwhile, included what was called "Physics". ''Greek concept'' The move towards a rational understanding of nature began at least since the Archaic period in Greece (650–480 BCE) with the Pre-Socratic philosophers. The philosopher Thales of Miletus (7th and 6th centuries BCE), dubbed "the Father of Science" for refusing to accept various supernatural, religious or mythological ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Quantum Mechanics
The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be ''discrete''; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ''ε'' (Greek letter epsilon) such that each of these energy elements is proportional to the frequency ''ν'' with which each of them individually radiate energy, as defined by the following formula: : \varepsilon = h \nu, where ''h'' is a numerical value called Planck' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visible Spectrum Of Hydrogen
Visibility, in meteorology, is a measure of the distance at which an object or light can be seen. Visibility may also refer to: * A measure of turbidity in water quality control * Interferometric visibility, which quantifies interference contrast in optics * The reach of information hiding, in computing * Visibility (geometry), a geometric abstraction of real-life visibility * Visible spectrum, the portion of the electromagnetic spectrum that is visible to the human eye * Visual perception ** Naked-eye visibility Visible may also refer to: * ''Visible'' (album), a 1985 album by CANO * '' Visible: Out on Television'', a 2020 miniseries from Apple TV+, about LGBTQ+ representation in TV * Visible spectrum, light which can be seen by the human eye * Visible (wireless service), an offshoot phone service from Verizon Communications See also * * * Transparency (other) * Vis (other) * Vision (other) Vision, Visions, or The Vision may refer to: Percept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Variables
Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty relation corresponds to the symplectic form. Also, conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate variable will not change with time (i.e. it will be conserved). Examples There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following: * Time and frequency: the longer a musical note is sustained, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it 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 Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distributi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H Plasma Spectrum
H, or h, is the eighth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''aitch'' (pronounced , plural ''aitches''), or regionally ''haitch'' ."H" '' Oxford English Dictionary,'' 2nd edition (1989); ''Merriam-Webster's Third New International Dictionary of the English Language, Unabridged'' (1993); "aitch" or "haitch", op. cit. History The original Semitic letter Heth most likely represented the voiceless pharyngeal fricative (). The form of the letter probably stood for a fence or posts. The Greek Eta 'Η' in archaic Greek alphabets, before coming to represent a long vowel, , still represented a similar sound, the voiceless glottal fricative . In this context, the letter eta is also known as Heta to underline this fact. Thus, in the Old Italic alphabets, the letter Heta of the Euboean alphabet was adopted with its original sound value . While Etrusc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford Dictionary Of National Biography
The ''Dictionary of National Biography'' (''DNB'') is a standard work of reference on notable figures from British history, published since 1885. The updated ''Oxford Dictionary of National Biography'' (''ODNB'') was published on 23 September 2004 in 60 volumes and online, with 50,113 biographical articles covering 54,922 lives. First series Hoping to emulate national biographical collections published elsewhere in Europe, such as the '' Allgemeine Deutsche Biographie'' (1875), in 1882 the publisher George Smith (1824–1901), of Smith, Elder & Co., planned a universal dictionary that would include biographical entries on individuals from world history. He approached Leslie Stephen, then editor of the '' Cornhill Magazine'', owned by Smith, to become the editor. Stephen persuaded Smith that the work should focus only on subjects from the United Kingdom and its present and former colonies. An early working title was the ''Biographia Britannica'', the name of an earlier eig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the University of Cambridge, a professor of physics at Florida State University and the University of Miami, and a 1933 Nobel Prize recipient. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics. Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative Property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as ''noncommutative operations''. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
