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Few-body Systems
In mechanics, a few-body system consists of a small number of well-defined structures or point particles. Quantum mechanics In quantum mechanics, examples of few-body systems include light nuclear systems (that is, few-nucleon bound and scattering states), small molecules, light atoms (such as helium in an external electric field), atomic collisions, and quantum dots. A fundamental difficulty in describing few-body systems is that the Schrödinger equation and the classical equations of motion are not analytically solvable for more than two mutually interacting particles even when the underlying forces are precisely known. This is known as the few-body problem. For some three-body systems an exact solution can be obtained iteratively through the Faddeev equations. It can be shown that under certain conditions Faddeev equations should lead to Efimov effect. Some special cases of three-body systems are amenable to analytical solutions (or nearly so) - by special treatments ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects result in displacements, or changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, Huygens, and Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Efimov Effect
Yefimov, sometimes spelled Efimov (russian: Ефимов), or Yefimova (feminine; Ефимова) is a Russian last name and may refer to: * Alexander Yefimov (1923–2012), a Soviet aircraft pilot and twice Hero of the Soviet Union * Boris Efimov Boris Yefimovich Yefimov (russian: Бори́с Ефи́мович Ефи́мов; ,The birth record of Boris Fridlyand (Boris Yefimov) in the metric book of the Kiev rabbinate for 1900 ( ЦГИАК Украины. Ф. 1164. Оп. 1. Д. 454. Л. ... (1900–2008), a Soviet political cartoonist and propaganda artist * Igor Yefimov (1937–2020), an American philosopher, writer, and publisher of Russian origin * Mikhail Efimov (1881–1919), a Russian aviation pioneer *: 2754 Efimov, an asteroid named after Mikhail Efimov * Mikhail Yefimov (born 1978), Russian football player * Nikolai Efimov (1910–1982), a Russian mathematician * Sergei Yefimov (1922–1994), a Soviet army officer and Hero of the Soviet Union * Sergei Efimov (bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Physical Society
The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of knowledge of physics. The society publishes more than a dozen scientific journals, including the prestigious '' Physical Review'' and '' Physical Review Letters'', and organizes more than twenty science meetings each year. APS is a member society of the American Institute of Physics. Since January 2021 the organization has been led by chief executive officer Jonathan Bagger. History The American Physical Society was founded on May 20, 1899, when thirty-six physicists gathered at Columbia University for that purpose. They proclaimed the mission of the new Society to be "to advance and diffuse the knowledge of physics", and in one way or another the APS has been at that task ever since. In the early years, virtually the sole activity of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Few Body Topical Group
Few may refer to: People * Bobby Few (1935–2021), an American musician * Francis E. Walter, an American politician from Pennsylvania * Ignatius Alphonso Few (1789–1845), an American preacher and academic, first president of Emory College (now Emory University) * Mark Few (born 1962), an American basketball coach * Robyn Few (1958–2012), an American rights activist * William Few (1748–1828), an American founding father from Georgia * William Preston Few (1867–1940), the first president of Duke University Other uses * The Few, British aviators in the Battle of Britain * Few (album), fifth studio album by rock band He is Legend * Francis E. Walter Dam, a dam, recreational area, and disc golf course in Pennsylvania * French Engineering Works, a South African tool manufacturer * FEW, Französisches Etymologisches Wörterbuch (German: French Etymological Dictionary) See also * Chosen Few (other) * Quantity Quantity or amount is a property that can exist as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Problem
In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the -body problem, especially Ms. Kovalevskaya's 1868–1888 twenty-year complex-variables approach, failure; Section 1: "The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics" (Chapter 1, "The motion of a rigid body about a fixed point (Euler and Poisson equations)"; Chapter 2, "Mathematical Exterior Ballistics"), good precursor background to the -body problem; Section 2: "Celestial Mechanics" (Chapter 1, "The Uniformization of the Three-body Problem (Restricted Three-body Problem)"; Chapter 2, "Capture in the Three-Body Problem"; Chapter 3, "Generalized -body Problem"). Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In the 20th century, und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematically Complete Experiment
In accelerator physics, a kinematically complete experiment is an experiment in which all kinematic parameters of all collision products are determined. If the final state of the collision involves n particles 3n momentum components (3 Cartesian coordinates for each particle) need to be determined. However, these components are linked to each other by momentum conservation in each direction (3 equations) and energy conservation (1 equation) so that only 3n-4 components are linearly independent. Therefore, the measurement of 3n-4 momentum components constitutes a kinematically complete experiment. If the final state involves only two particles (e.g. in the Rutherford experiment on elastic scattering) then only one particle needs to be detected. However, for processes leading to three collision products, like e.g. single ionization of the target atom, then two particles need to be momentum-analyzed (for one of them it is sufficient to measure two momentum components) and measur ... [...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 \nabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambert W Function
In mathematics, the Lambert function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function , where is any complex number and is the exponential function. For each integer there is one branch, denoted by , which is a complex-valued function of one complex argument. is known as the principal branch. These functions have the following property: if and are any complex numbers, then :w e^ = z holds if and only if :w=W_k(z) \ \ \text k. When dealing with real numbers only, the two branches and suffice: for real numbers and the equation :y e^ = x can be solved for only if ; we get if and the two values and if . The Lambert relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance, in the enumeration of trees. It can be used to solve various equations involving exponentials (e.g. the maxima of the Planck, Bose–Einstein, and Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dihydrogen Cation
The dihydrogen cation or hydrogen molecular ion is a cation (positive ion) with formula . It consists of two hydrogen nuclei ( protons) sharing a single electron. It is the simplest molecular ion. The ion can be formed from the ionization of a neutral hydrogen molecule . It is commonly formed in molecular clouds in space, by the action of cosmic rays. The dihydrogen cation is of great historical and theoretical interest because, having only one electron, the equations of quantum mechanics that describe its structure can be solved in a relatively straightforward way. The first such solution was derived by Ø. Burrau in 1927, just one year after the wave theory of quantum mechanics was published. Physical properties Bonding in can be described as a covalent one-electron bond, which has a formal bond order of one half. The ground state energy of the ion is -0.597 Hartree. Isotopologues The dihydrogen cation has six isotopologues, that result from replacement of one o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faddeev Equations
The Faddeev equations, named after their inventor Ludvig Faddeev, are equations that describe, at once, all the possible exchanges/interactions in a system of three particles in a fully quantum mechanical formulation. They can be solved iteratively. In general, Faddeev equations need as input a potential that describes the interaction between two individual particles. It is also possible to introduce a term in the equation in order to take also three-body forces into account. The Faddeev equations are the most often used non-perturbative formulations of the quantum-mechanical three-body problem. Unlike the three body problem in classical mechanics, the quantum three body problem is uniformly soluble. In nuclear physics, the off the energy shell nucleon-nucleon interaction has been studied by analyzing (n,2n) and (p,2p) reactions on deuterium targets, using the Faddeev Equations. The nucleon-nucleon interaction is expanded (approximated) as a series of separable potentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Particle
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space. A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. Point masses and point charges, discussed below, are two common cases. When a point particle has an additive property, such as mass or charge, it is often represented mathematically by a Dirac delta function. In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. For example, the atomic orbit of an electron in the hydrogen atom occupies a volume of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
