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Born Approximation
Generally in scattering theory and in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. The Born approximation is named after Max Born who proposed this approximation in the early days of quantum theory development. It is the perturbation method applied to scattering by an extended body. It is accurate if the scattered field is small compared to the incident field on the scatterer. For example, the scattering of radio waves by a light styrofoam column can be approximated by assuming that each part of the plastic is polarized by the same electric field that would be present at that point without the column, and then calculating the scattering as a radiation integral over that polarization distribution. Approximate scattering amplitude Starting with a physical model based on the Schrodinger wave equation for scattering from a potential the scattering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born–Oppenheimer Approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are much heavier than the electrons. Due to the larger relative mass of a nucleus compared to an electron, the coordinates of the nuclei in a system are approximated as fixed, while the coordinates of the electrons are dynamic. The approach is named after Max Born and his 23-year-old graduate student J. Robert Oppenheimer, the latter of whom proposed it in 1927 during a period of intense ferment in the development of quantum mechanics. The approximation is widely used in quantum chemistry to speed up the computation of molecular wavefunctions and other properties for large molecules. There are cases where the assumption of separable motion no longer holds, which make the approximation lose validity (it is said to "break down"), but even then the ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Series
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyson Series
In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams. This series diverges asymptotically, but in quantum electrodynamics (QED) at the second order the difference from experimental data is in the order of 10−10. This close agreement holds because the coupling constant (also known as the fine-structure constant) of QED is much less than 1. Dyson operator In the interaction picture, a Hamiltonian , can be split into a ''free'' part and an ''interacting part'' as . The potential in the interacting picture is :V_(t) = \mathrm^ V_(t) \mathrm^, where H_0 is time-independent and V_(t) is the possibly time-dependent interacting part of the Schrödinger picture. To avoid subscripts, V(t) stands for V_\mathrm(t) in what follows. In the interaction picture, the evolution oper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photoelectric Effect
The photoelectric effect is the emission of electrons from a material caused by electromagnetic radiation such as ultraviolet light. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, solid state, and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. The effect has found use in electronic devices specialized for light detection and precisely timed electron emission. The experimental results disagree with classical electromagnetism, which predicts that continuous light waves transfer energy to electrons, which would then be emitted when they accumulate enough energy. An alteration in the intensity of light would theoretically change the kinetic energy of the emitted electrons, with sufficiently dim light resulting in a delayed emission. The experimental results instead show that electrons are dislodged only when the light exceeds a certain frequency—regardless of the ligh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bremsstrahlung
In particle physics, bremsstrahlung (; ; ) is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., photons), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases. Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the acceleration (positive or negative) of a charged particle, which includes synchrotron radiation (i.e., photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Wave
In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ..., a plane wave is a special case of a wave or field: a physical quantity whose value, at any given moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, the value of such a field can be written as F(\vec x,t) = G(\vec x \cdot \vec n, t), where \vec n is a unit-length vector, and G(d,t) is a function that gives the field's value as dependent on only two real parameters: the time t, and the scalar-valued displacement d = \vec x \cdot \vec n of the point \vec x along the direction \vec n. The displacement is constant over each plane perpendicular to \vec n. The values of the field F may be scalars, vectors, or any other physical or ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seismic Waves
A seismic wave is a mechanical wave of acoustic wave, acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake (natural phenomenon), quake), types of volcanic eruptions, volcanic eruption, magma movement, a large landslide and a large man-made explosion that produces low-frequency acoustic energy. Seismic waves are studied by seismology, seismologists, who record the waves using seismometers, hydrophones (in water), or accelerometers. Seismic waves are distinguished from seismic noise (ambient vibration), which is persistent low-amplitude vibration arising from a variety of natural and anthropogenic sources. The signal velocity, propagation velocity of a seismic wave depends on density and elasticity (physics), elasticity of the medium as well as the type of wave. Velocity tends to increase with depth through Earth's crust (geology), crust and mantle (geology), mantle, but drops sharply going from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Elasticity
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed by prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental assumptions of linear elasticity are infinitesimal strains — meaning, "small" deformations — and linear relationships between the components of stress and strain — hence the "linear" in its name. Linear elasticity is valid only for stress states that do not produce yielding. Its assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis. Mathematical formulation Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilayer Graphene
Bilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 ''Science'' paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers" Structure Bilayer graphene can exist in the AB, or Bernal-stacked form, where half of the atoms lie directly over the center of a hexagon in the lower graphene sheet, and half of the atoms lie over an atom, or, less commonly, in the AA form, in which the layers are exactly aligned. In Bernal stacked graphene, twin boundaries are common; transitioning from AB to BA stacking. Twisted layers, where one layer is rotated relative to the other, have also been extensively studied. Quantum Monte Carlo methods have been used to calculate the binding energies of AA- and AB-stacked bilayer graphene, which are 11.5(9) and 17.7(9) meV per atom, respectively. This is consistent with the observation that the AB-stacked structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monolayer
A monolayer is a single, closely packed layer of entities, commonly atoms or molecules. Monolayers can also be made out of cells. ''Self-assembled monolayers'' form spontaneously on surfaces. Monolayers of layered crystals like graphene and molybdenum disulfide are generally called '' 2D materials''. Types A Langmuir monolayer or ''insoluble monolayer'' is a one-molecule thick layer of an insoluble organic material spread onto an aqueous subphase in a Langmuir–Blodgett trough. Traditional compounds used to prepare Langmuir monolayers are amphiphilic materials that possess a hydrophilic headgroup and a hydrophobic tail. Since the 1980s a large number of other materials have been employed to produce Langmuir monolayers, some of which are semi-amphiphilic, including polymeric, ceramic or metallic nanoparticles and macromolecules such as polymers. Langmuir monolayers are extensively studied for the fabrication of Langmuir–Blodgett film (LB films), which are formed by transf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grazing-incidence Small-angle Scattering
Grazing-incidence small-angle scattering (GISAS) is a scattering technique used to study nanostructured surfaces and thin films. The scattered probe is either photons (grazing-incidence small-angle X-ray scattering, GISAXS) or neutrons (grazing-incidence small-angle neutron scattering, GISANS). GISAS combines the accessible length scales of small-angle scattering (SAS: SAXS or SANS) and the surface sensitivity of grazing incidence diffraction (GID). Applications A typical application of GISAS is the characterisation of self-assembly and self-organization on the nanoscale in thin films. Systems studied by GISAS include quantum dot arrays, growth instabilities formed during in-situ growth, self-organized nanostructures in thin films of block copolymers, silica mesophases, and nanoparticles. GISAXS was introduced by Levine and Cohen to study the dewetting of gold deposited on a glass surface. The technique was further developed by Naudon and coworkers to study metal agglomerates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutron Guide
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The neutron was discovered by James Chadwick in 1932, leading to the discovery of nuclear fission in 1938, the first self-sustaining nuclear reactor (Chicago Pile-1, 1942) and the first nuclear weapon (Trinity, 1945). Neutrons are found, together with a similar number of protons in the nuclei of atoms. Atoms of a chemical element that differ only in neutron number are called isotopes. Free neutrons are produced copiously in nuclear fission and fusion. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes. Neutron stars, formed from massive collapsing stars, consist of neutrons at the density of atomic nuclei but a total mass more than the Sun. Neutron properties and interactions are described by nuclear physics. Neutrons are not elementary particles; each is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
