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 was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] 

Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary ( macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves ( wave–particle duality); and there are lim ... [...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 inflammation in the nose that occurs when the immune system overreacts to allergens in the air. 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 siblings decreases this risk. The underlying mechanism involves IgE antibodie ... [...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 in the literature we find also other symbols for the position operator, for instance Q (from Lagrangian mechanics), \hat \mathrm x and so on 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 \ ... [...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 through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visible light, ultraviolet, xrays, and gamma radiation (γ) * '' particle radiation'', such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation (particles of nonzero rest energy) * '' acoustic radiation'', such as ultrasound, sound, and seismic waves (dependent on a physical transmission medium) * '' gravitational radiation'', that takes the form of gravitational waves, or ripples in the curvature of spacetime Radiation is often categorized as either '' ionizing'' or ''nonionizing'' depending on the energy of the radiated particles. Ionizing radiation carries more than 10 eV, which is enough to ionize atoms and molecules and break chemical bonds. This is an important distinction due to the large diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] 

Correspondence Principle
In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations. The principle was formulated by Niels Bohr in 1920, though he had previously made use of it as early as 1913 in developing his model of the atom. The term codifies the idea that a new theory should reproduce under some conditions the results of older wellestablished theories in those domains where the old theories work. This concept is somewhat different from the requirement of a formal limit under which the new theory reduces to the older, thanks to the existence of a deformation parameter. Classical quantities appear in quantum mechanics in the form of expected values of observables, and as such the Ehrenfest theorem (whic ... [...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 selfconsistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semiclassical 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 which were both premised on the Arnold Sommerfeld 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 selecting out certain states of a classical system as allowed states: 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] 

Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete ... [...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] 

Über Quantentheoretische Umdeutung Kinematischer Und Mechanischer Beziehungen
("Quantum theoretical reinterpretation of kinematic and mechanical relations") was a breakthrough article in quantum mechanics written by Werner Heisenberg, which appeared in ''Zeitschrift für Physik'' in September 1925. Heisenberg worked on the article while recovering from hay fever on the island of Heligoland, corresponding with Wolfgang Pauli on the subject. When asked for his opinion of the manuscript, Pauli responded favorably, but Heisenberg said that he was still "very uncertain about it". In July 1925, he sent the manuscript to Max Born to review and decide whether to submit it for publication. In the article, Heisenberg tried to explain the energy levels of a onedimensional 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. Also included was the ''Hei ... [...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. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] 