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Araki–Sucher Correction
In atomic, molecular and optical physics, the Araki–Sucher correction is a leading-order correction to the energy levels of atoms and molecules due to effects of quantum electrodynamics (QED). It is named after Huzihiro Araki and Joseph Sucher, who first calculated it for the helium atom in 1957. The method is based on a perturbative expansion of the energy in the Bethe–Salpeter equation, and have since been used to calculate corrections for atoms other than helium (e.g. beryllium and lithium), and for systems with more than two electrons. The correction typically involves the fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ... \alpha and may sometimes include terms of third order and higher . References Eponymous equations of physics Quantum mecha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic, Molecular, And Optical Physics
Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments. Typically, the theory and applications of emission, absorption, scattering of electromagnetic radiation (light) from excited atoms and molecules, analysis of spectroscopy, generation of lasers and masers, and the optical properties of matter in general, fall into these categories. Atomic and molecular physics Atomic physics is the subfield of AMO that studies atoms as an isolated system of electrons and an atomic nucleus, while molecular physics is the study of the physical properties of molecules. The term ''atomic physics'' is often associated with nuclear power and nuclear bombs, due to the synonymous use of ''atomic'' and ''nuclear'' in standard English. However, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Level
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized. In chemistry and atomic physics, an electron shell, or principal energy level, may be thought of as the orbit of one or more electrons around an atom's nucleus. The closest shell to the nucleus is called the " shell" (also called "K shell"), followed by the " shell" (or "L shell"), then the " shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huzihiro Araki
is a Japanese mathematical physicist and mathematician, who worked on the foundations of quantum field theory, on quantum statistical mechanics, and on the theory of operator algebras. Biography Araki is the son of the University of Kyoto physics professor Gentarō Araki, with whom he studied and with whom in 1954 he published his first physics paper. He earned his diploma under Hideki Yukawa and in 1960 he attained his doctorate at Princeton University with thesis advisors Rudolf Haag and Arthur Wightman. Since 1966 he was a professor at the University of Kyoto, at the Research Institute for Mathematical Sciences (RIMS), of which he was also the director. Araki works on axiomatic quantum field theory, statistical mechanics, and in particular on applications of operator algebras like von Neumann algebras and C*-algebras. At the beginning of the 1960s, in Princeton, he made important contributions to local quantum physics and to the scattering theories of Haag and David Ruell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helium Atom
A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with either one or two neutrons, depending on the isotope, held together by the strong force. Unlike for hydrogen, a closed-form solution to the Schrödinger equation for the helium atom has not been found. However, various approximations, such as the Hartree–Fock method, can be used to estimate the ground state energy and wavefunction of the atom. Introduction The quantum mechanical description of the helium atom is of special interest, because it is the simplest multi-electron system and can be used to understand the concept of quantum entanglement. The Hamiltonian of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as H(\mathbf_1,\, \mathbf_2) = \sum_\left(-\frac \nabla^2_ -\frac\right) - \frac \nabla_ \cdot \nab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bethe–Salpeter Equation
The Bethe–Salpeter equation (named after Hans Bethe and Edwin Salpeter) describes the bound states of a two-body (particles) quantum field theoretical system in a relativistically covariant formalism. The equation was actually first published in 1950 at the end of a paper by Yoichiro Nambu, but without derivation. Due to its generality and its application in many branches of theoretical physics, the Bethe–Salpeter equation appears in many different forms. One form, that is quite often used in high energy physics is : \Gamma(P,p) =\int\!\frac \; K(P,p,k)\, S(k-\tfrac) \,\Gamma(P,k)\, S(k+\tfrac) where ''Γ'' is the Bethe–Salpeter amplitude, ''K'' the interaction and ''S'' the propagators of the two participating particles. In quantum theory, bound states are objects with lifetimes that are much longer than the time-scale of the interaction ruling their structure (otherwise they are called resonances). Thus the constituents interact essentially infinitely many times ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beryllium
Beryllium is a chemical element with the symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form minerals. Notable gemstones high in beryllium include beryl ( aquamarine, emerald) and chrysoberyl. It is a relatively rare element in the universe, usually occurring as a product of the spallation of larger atomic nuclei that have collided with cosmic rays. Within the cores of stars, beryllium is depleted as it is fused into heavier elements. Beryllium constitutes about 0.0004 percent by mass of Earth's crust. The world's annual beryllium production of 220 tons is usually manufactured by extraction from the mineral beryl, a difficult process because beryllium bonds strongly to oxygen. In structural applications, the combination of high flexural rigidity, thermal stability, thermal conductivity and low density (1.85 times that of wate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lithium
Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid element. Like all alkali metals, lithium is highly reactive and flammable, and must be stored in vacuum, inert atmosphere, or inert liquid such as purified kerosene or mineral oil. When cut, it exhibits a metallic luster, but moist air corrodes it quickly to a dull silvery gray, then black tarnish. It never occurs freely in nature, but only in (usually ionic) compounds, such as pegmatitic minerals, which were once the main source of lithium. Due to its solubility as an ion, it is present in ocean water and is commonly obtained from brines. Lithium metal is isolated electrolytically from a mixture of lithium chloride and potassium chloride. The nucleus of the lithium atom verges on instability, since the two stable lithium isotopes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, per the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fine-structure Constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge ''e'' with the electromagnetic field, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by Arnold Sommerfeld, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the Bohr model of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887. Definition In terms of other fundamental physical constants, may be defined as: \alpha = \frac = \frac , where * is the elementary c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eponymous Equations Of Physics
An eponym is a person, a place, or a thing after whom or which someone or something is, or is believed to be, named. The adjectives which are derived from the word eponym include ''eponymous'' and ''eponymic''. Usage of the word The term ''eponym'' functions in multiple related ways, all based on an explicit relationship between two named things. A person, place, or thing named after a particular person share an eponymous relationship. In this way, Elizabeth I of England is the eponym of the Elizabethan era. When Henry Ford is referred to as "the ''eponymous'' founder of the Ford Motor Company", his surname "Ford" serves as the eponym. The term also refers to the title character of a fictional work (such as Rocky Balboa of the ''Rocky'' film series), as well as to ''self-titled'' works named after their creators (such as the album ''The Doors'' by the band the Doors). Walt Disney created the eponymous Walt Disney Company, with his name similarly extended to theme parks such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
