|
Fermi Pseudopotential
In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering. The pseudopotential approximation was first introduced by Hans Hellmann in 1934. Atomic physics The pseudopotential is an attempt to replace the complicated effects of the motion of the Core electron, core (i.e. non-Valence electron, valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulomb's law, Coulombic potential term for core electrons normally found in the Schrödinger equation. The pseudopotential is an effective potential constructed to replace the atomic all-electron potential (full-potential) such that core states are eliminated ''and'' the valence electrons are described by pseudo-wavefunctions with significantly fewer nodes. This allows the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sketch Pseudopotentials
Sketch or Sketches may refer to: * Sketch (drawing), a rapidly executed freehand drawing that is not usually intended as a finished work Arts, entertainment and media * Sketch comedy, a series of short scenes or vignettes called sketches Film and television * Sketch (2007 film), ''Sketch'' (2007 film), a Malayalam film * Sketch (2018 film), ''Sketch'' (2018 film), a Tamil film * Sketch (2024 film), ''Sketch'' (2024 film), an American comedy horror film * Sketch (TV series), ''Sketch'' (TV series), a 2018 South Korean series * "Sketch", a 2008 List of Skins episodes#Series 2 (2008), episode of ''Skins'' ** Sketch (Skins character), Sketch (''Skins'' character) * Sketch with Kevin McDonald, a 2006 CBC television special Literature * Sketch story, or sketch, a very short piece of writing * ''Daily Sketch'', a British newspaper 1909–1971 * ''The Sketch'', a British illustrated weekly journal 1893–1959 Music * Sketch (music), an informal document prepared by a composer to as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearized Augmented-plane-wave Method
The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation. This is often referred to as the all-electron full-potential linearized augmented-plane-wave method (FLAPW). It does not rely on the pseudopotential approximation and employs a systematically extendable basis set. These features make it one of the most precise implementations of DFT, applicable to all crystalline materials, regardless of their chemical composition. It can be used as a reference for evaluating other approaches. Introduction At the core of density functional theory the Hohenberg-Kohn theorems state that every observable of an interacting many-electron system is a functional of its ground-state charge density a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Form Factor
In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray diffraction, X-ray, Electron diffraction, electron or Neutron diffraction, neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from space, real space to momentum space (also known as reciprocal space). For an object with spatial density distribution, \rho(\mathbf), the form factor, f(\mathbf), is defined as :f(\mathbf)=\int \rho(\mathbf) e^\mathrm^3\mathbf, where \rho(\mathbf) is the spatial density of the scatterer about its center of mass (\mathbf=0), and \mathbf is the momentum transfer. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer \rho in real space \mathbf, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester based on the 1909 Geiger–Marsden experiments, Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of () for hydrogen (the diameter of a single proton) to about for uranium. These dimensions are much ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the Phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering Length
The scattering length in quantum mechanics describes low-energy scattering. For potentials that decay faster than 1/r^3 as r\to \infty, it is defined as the following low-energy limit: : \lim_ k\cot\delta(k) =- \frac\;, where a is the scattering length, k is the wave number, and \delta(k) is the phase shift of the outgoing spherical wave. The elastic cross section, \sigma_e, at low energies is determined solely by the scattering length: : \lim_ \sigma_e = 4\pi a^2\;. General concept When a slow particle scatters off a short ranged scatterer (e.g. an impurity in a solid or a heavy particle) it cannot resolve the structure of the object since its de Broglie wavelength is very long. The idea is that then it should not be important what precise potential V(r) one scatters off, but only how the potential looks at long length scales. The formal way to solve this problem is to do a partial wave expansion (somewhat analogous to the multipole expansion in classical electrodyna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta Function
In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. Thus it can be Heuristic, represented heuristically as \delta (x) = \begin 0, & x \neq 0 \\ , & x = 0 \end such that \int_^ \delta(x) dx=1. Since there is no function having this property, modelling the delta "function" rigorously involves the use of limit (mathematics), limits or, as is common in mathematics, measure theory and the theory of distribution (mathematics), distributions. The delta function was introduced by physicist Paul Dirac, and has since been applied routinely in physics and engineering to model point masses and instantaneous impulses. It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particle, elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple Mass in special relativity, definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure (mathematics), measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the Force, strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is Mass versus weight, not the same as weight, even though mass is often determined by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck Constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum. The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Planck later referred to the constant as the "quantum of Action (physics), action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave itself. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". In metrology, the Planck constant 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, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Wave Analysis
Partial-wave analysis, in the context of quantum mechanics, refers to a technique for solving scattering problems by decomposing each wave into its constituent angular-momentum components and solving using boundary conditions. Partial wave analysis is typically useful for low energy scattering where only a few angular momentum components dominate. At high energy were scattering is weak, an alternative called the Born approximation is used. Preliminary scattering theory A steady beam of particles scatters off a spherically symmetric potential V(r), which is short-ranged, so that for large distances r \to \infty, the particles behave like free particles. The incoming beam is assumed to be a collimated plane wave \exp(ikz) traveling along the ''z'' axis. Because the beam is switched on for times long compared to the time of interaction of the particles with the scattering potential, a steady state is assumed. This means that the stationary Schrödinger equation for the wave f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enrico Fermi
Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian and naturalized American physicist, renowned for being the creator of the world's first artificial nuclear reactor, the Chicago Pile-1, and a member of the Manhattan Project. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics, theoretical and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, Quantum mechanics, quantum theory, and nuclear physics, nuclear and particle physics. Fermi's first major contribution involved the field of statistical mechanics. Afte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projector Augmented Wave Method
The projector augmented wave method (PAW) is a technique used in ab initio electronic structure calculations. It is a generalization of the pseudopotential and linear augmented-plane-wave methods, and allows for density functional theory calculations to be performed with greater computational efficiency. Valence wavefunctions tend to have rapid oscillations near ion cores due to the requirement that they be orthogonal to core states; this situation is problematic because it requires many Fourier components (or in the case of grid-based methods, a very fine mesh) to describe the wavefunctions accurately. The PAW approach addresses this issue by transforming these rapidly oscillating wavefunctions into smooth wavefunctions which are more computationally convenient, and provides a way to calculate all-electron properties from these smooth wavefunctions. This approach is somewhat reminiscent of a change from the Schrödinger picture to the Heisenberg picture. Transforming the wavef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
