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Matrix Mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. Development of matrix mechanics In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland In 1925 Werner Heisenberg w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hay Fever
Allergic rhinitis, of which the seasonal type is called hay fever, is a type of rhinitis, inflammation in the nose that occurs when the immune system overreacts to allergens in the air. It is classified as a Allergy, type I hypersensitivity reaction. Signs and symptoms include a runny or stuffy nose, sneezing, red, itchy, and watery eyes, and swelling around the eyes. The fluid from the nose is usually clear. Symptom onset is often within minutes following allergen exposure, and can affect sleep and the ability to work or study. Some people may develop symptoms only during specific times of the year, often as a result of pollen exposure. Many people with allergic rhinitis also have asthma, allergic conjunctivitis, or atopic dermatitis. Allergic rhinitis is typically triggered by environmental allergens such as pollen, pet hair, dust, or mold. Inherited genetics and environmental exposures contribute to the development of allergies. Growing up on a farm and having multiple olde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Rosanes
Jakob Rosanes (also Jacob; 16 August 1842 – 6 January 1922) was a German mathematician who worked on algebraic geometry and invariant theory. He was also a chess master. Life and career Rosanes was a grandson of Rabbi Akiva Eiger, one of the most revered Jewish religious scholars of the Talmud and ''halachic'' decisors of the 18th century. Eiger's daughter Baila was Rosanes' mother. Rosanes grew up during a period when the Enlightenment and increasing opportunities for social, academic and economic advancement for culturally assimilated Jews influenced large numbers of Jews to reconsider their faith. He was not religiously observant, and his children converted to Christianity. Rosanes studied at University of Berlin and the University of Breslau. He obtained his doctorate from Breslau (Wrocław) in 1865 and taught there for the rest of his working life. He became professor in 1876 and rector of the university during the years 1903–1904. In his ‘inspiring’ rectorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position Operator
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle. In one dimension, if by the symbol , x \rangle we denote the unitary eigenvector of the position operator corresponding to the eigenvalue x, then, , x \rangle represents the state of the particle in which we know with certainty to find the particle itself at position x. Therefore, denoting the position operator by the symbol X we can write X, x\rangle = x , x\rangle, for every real position x. One possible realization of the unitary state with position x is the Dirac delta (function) distribution centered at the position x, often denoted by \delta_x. In quantum mechanics, the ordered (continuous) family of all Dirac distributions, i.e. the family \delta = (\delta_x)_, is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and Gamma ray, gamma radiation (γ) * ''particle radiation'' consisting of particles of non-zero rest energy, such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation * ''acoustics, acoustic radiation'', such as ultrasound, sound, and seismic waves, all dependent on a physical transmission medium * ''gravitational radiation'', in the form of gravitational waves, ripples in spacetime Radiation is often categorized as either ''ionizing radiation, ionizing'' or ''non-ionizing radiation, non-ionizing'' depending on the energy of the radiated particles. Ionizing radiation carries more than 10 electron volt, electron volts (eV), which is enough to ionize atoms and molecul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correspondence Principle
In physics, a correspondence principle is any one of several premises or assertions about the relationship between classical and quantum mechanics. The physicist Niels Bohr coined the term in 1920 during the early development of quantum theory; he used it to explain how quantized classical orbitals connect to quantum radiation. Modern sources often use the term for the idea that the behavior of systems described by quantum theory reproduces classical physics in the limit of large quantum numbers: for large orbits and for large energies, quantum calculations must agree with classical calculations. A "generalized" correspondence principle refers to the requirement for a broad set of connections between any old and new theory. History Max Planck was the first to introduce the idea of quanta of energy, while studying black-body radiation in 1900. In 1906, he was also the first to write that quantum theory should replicate classical mechanics at some limit, particularly if the Pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Quantum Theory
The old quantum theory is a collection of results from the years 1900–1925, which predate modern quantum mechanics. The theory was never complete or self-consistent, but was instead a set of heuristic corrections to classical mechanics. The theory has come to be understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by Edmund Stoner and the Pauli exclusion principle, both of which were premised on Arnold Sommerfeld's enhancements to the Bohr model of the atom. The main tool of the old quantum theory was the Bohr–Sommerfeld quantization condition, a procedure for selection of certain allowed states of a classical system: the system can then only exist in one of the allowed states and not in any other state. History The old quantum theory was instigated by the 1900 work of Max Planck on the emission and absorption of light in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
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] |
Hendrik Kramers
Hendrik Anthony "Hans" Kramers (17 December 1894 – 24 April 1952) was a Dutch physicist who worked with Niels Bohr to understand how electromagnetic waves interact with matter and made important contributions to quantum mechanics and statistical physics. Background and education Hans Kramers was born on 17 December 1894 in Rotterdam. the son of Hendrik Kramers, a physician, and Jeanne Susanne Breukelman. In 1912 Hans finished secondary education ( HBS) in Rotterdam, and studied mathematics and physics at the University of Leiden, where he obtained a master's degree in 1916. Kramers wanted to obtain foreign experience during his doctoral research, but his first choice of supervisor, Max Born in Göttingen, was not reachable because of the First World War. Because Denmark was neutral in this war, as was the Netherlands, he travelled (by ship, overland was impossible) to Copenhagen, where he visited unannounced the then still relatively unknown Niels Bohr. Bohr took him on as a Ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ãœber Quantentheoretische Umdeutung Kinematischer Und Mechanischer Beziehungen
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 configuration, 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 Max Born and Pascual Jordan of the same year, and by the 'three-man paper' () by Born, Heisenberg and J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutativity
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. Perhaps most familiar as a property of arithmetic, e.g. 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 centuries implicitly assumed. Thus, this property was not named until the 19th century, when new algebraic structures started to be studied. Definition A binary operation * on a set ''S'' is ''commutative'' if x * y = y * x for all x,y \in S. An operation that is not commutative is said to be ''noncommutative''. One says ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
