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Debye–Waller Factor
The Debye–Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering or coherent neutron scattering caused by thermal motion. It is also called the B factor, atomic B factor, or temperature factor. Often, "Debye–Waller factor" is used as a generic term that comprises the Lamb–Mössbauer factor of incoherent neutron scattering and Mössbauer spectroscopy. The DWF depends on the scattering vector q. For a given q, DWF(q) gives the fraction of elastic scattering; 1 – DWF(q) correspondingly gives the fraction of inelastic scattering (strictly speaking, this probability interpretation is not true in general). In diffraction studies, only the elastic scattering is useful; in crystals, it gives rise to distinct Bragg reflection peaks. Inelastic scattering events are undesirable as they cause a diffuse background — unless the energies of scattered particles are analysed, in which case they c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Debye
Peter Joseph William Debye ( ; born Petrus Josephus Wilhelmus Debije, ; March 24, 1884 – November 2, 1966) was a Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry. Biography Early life Born in Maastricht, Netherlands, Debye enrolled in the Aachen University of Technology in 1901. In 1905, he completed his first degree in electrical engineering. He published his first paper, a mathematically elegant solution of a problem involving eddy currents, in 1907. At Aachen, he studied under the theoretical physicist Arnold Sommerfeld, who later claimed that his most important discovery was Peter Debye. In 1906, Sommerfeld received an appointment at Munich, Bavaria, and took Debye with him as his assistant. Debye got his Ph.D. with a dissertation on radiation pressure in 1908. In 1910, he derived the Planck radiation formula using a method which Max Planck agreed was simpler than his own. In 1911, when Albert Einstein took an appointment as a profes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Squared Displacement
In statistical mechanics, the mean squared displacement (MSD), also called mean square displacement, average squared displacement, or mean square fluctuation, is a measure of the deviation of the position of a particle with respect to a reference position over time. It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system "explored" by the random walker. In the realm of biophysics and environmental engineering, the MSD is measured over time to determine if a particle is spreading slowly due to diffusion, or if an advective force is also contributing. Another relevant concept, the variance-related diameter (VRD), defined as twice the square root of MSD, is also used in studying the transportation and mixing phenomena in environmental engineering. It prominently appears in the Debye–Waller factor (describing vibrations within the solid state) and in the Langevin equation (describing diffusion of a Brown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Summation Formula
In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function (mathematics), function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation. For a smooth, complex valued function s(x) on \mathbb R which decays at infinity with all derivatives (Schwartz function), the simplest version of the Poisson summation formula states that where S is the Fourier transform of s, i.e., S(f) \triangleq \int_^ s(x)\ e^\, dx. The summation formula can be restated in many equivalent ways, but a simple one is the following. Sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationary State
A stationary state is a quantum state with all observables independent of time. It is an eigenvector of the energy operator (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences explained below. Introduction A stationary state is called ''stationary'' because the system remains in the same state as time elapses, in every observable way. For a single-particle Hamiltonian, this means that the particle has a constant probability distribution for its position, its velocity, its spin, etc. (This is true assuming the particle's environment is also static, i.e. the Hamiltonian is unchanging in time.) The wavefunction itself is not stationary: It continually changes its overall complex phase factor, so as to form a standing wave. The oscillation frequency of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi's Golden Rule
In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a weak Perturbation theory (quantum mechanics), perturbation. This transition rate is effectively independent of time (so long as the strength of the perturbation is independent of time) and is proportional to the strength of the coupling between the initial and final states of the system (described by the square of the Matrix element (physics), matrix element of the perturbation) as well as the density of states. It is also applicable when the final state is discrete, i.e. it is not part of a continuum, if there is some decoherence in the process, like relaxation or collision of the atoms, or like noise in the perturbation, in which case the density of states is replaced by the reciprocal of the decoherence bandwidth. Historical background ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Momentum
In solid-state physics, crystal momentum or quasimomentum is a Momentum#Momentum in quantum mechanics, momentum-like Vector (geometric), vector associated with electrons in a Crystal structure, crystal lattice. It is defined by the associated Reciprocal lattice, wave vectors \mathbf of this lattice, according to \mathbf_ \equiv \hbar \mathbf (where \hbar is the reduced Planck constant). Frequently, crystal momentum is Momentum#Conservation, conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool. Lattice symmetry origins A common method of modeling crystal structure and behavior is to view electrons as Quantum mechanics, quantum mechanical particles traveling through a fixed infinite periodic potential V(x) such that V(\mathbf + \mathbf) = V(\mathbf), where \mathbf is an arbitrary Bravais lattice, lattice vector. Such a model is sensible because crystal Ion, ions that form the lattice structure are typically on the order ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Quantum Mechanics
''Modern Quantum Mechanics'', often called ''Sakurai'' or ''Sakurai and Napolitano'', is a standard graduate-level quantum mechanics textbook written originally by J. J. Sakurai and edited by San Fu Tuan in 1985, with later editions coauthored by Jim Napolitano. Sakurai died in 1982 before he could finish the textbook and both the first edition of the book, published in 1985 by Benjamin Cummings, and the revised edition of 1994, published by Addison-Wesley, were edited and completed by Tuan posthumously. The book was updated by Napolitano and released two later editions. The second edition was initially published by Addison-Wesley in 2010 and rereleased as an eBook by Cambridge University Press, who released a third edition in 2020. Table of contents (3rd edition) * Prefaces * Chapter 1: Fundamental Concepts * Chapter 2: Quantum Dynamics * Chapter 3: Theory of Angular Momentum * Chapter 4: Symmetry in Quantum Mechanics * Chapter 5: Approximation Methods * Chapter 6: Scattering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
External Links
An internal link is a type of hyperlink on a web page to another page or resource, such as an image or document, on the same website or domain. It is the opposite of an external link, a link that directs a user to content that is outside its domain. Hyperlinks are considered either "external" or "internal" depending on their target or destination. Generally, a link to a page outside the same domain or website is considered external, whereas one that points at another section of the same web page or to another page of the same website or domain is considered internal. Both internal and external links allow users of the website to navigate to another web page or resource. These definitions become clouded, however, when the same organization operates multiple domains functioning as a single web experience, e.g. when a secure commerce website is used for purchasing things displayed on a non-secure website. In these cases, links that are "external" by the above definition can conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutron
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, 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 (nuclear test), Trinity, 1945). Neutrons are found, together with a similar number of protons in the atomic nucleus, 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 nuclear fusion, 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-ray
An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ranging from 10 Nanometre, nanometers to 10 Picometre, picometers, corresponding to frequency, frequencies in the range of 30 Hertz, petahertz to 30 Hertz, exahertz ( to ) and photon energies in the range of 100 electronvolt, eV to 100 keV, respectively. X-rays were discovered in 1895 in science, 1895 by the German scientist Wilhelm Röntgen, Wilhelm Conrad Röntgen, who named it ''X-radiation'' to signify an unknown type of radiation.Novelline, Robert (1997). ''Squire's Fundamentals of Radiology''. Harvard University Press. 5th edition. . X-rays can penetrate many solid substances such as construction materials and living tissue, so X-ray radiography is widely used in medical diagnostics (e.g., checking for Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and " rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third cat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Protein Data Bank
The Protein Data Bank (PDB) is a database for the three-dimensional structural data of large biological molecules such as proteins and nucleic acids, which is overseen by the Worldwide Protein Data Bank (wwPDB). This structural data is obtained and deposited by biologists and biochemists worldwide through the use of experimental methodologies such as X-ray crystallography, Nuclear magnetic resonance spectroscopy of proteins, NMR spectroscopy, and, increasingly, cryo-electron microscopy. All submitted data are reviewed by expert Biocuration, biocurators and, once approved, are made freely available on the Internet under the CC0 Public Domain Dedication. Global access to the data is provided by the websites of the wwPDB member organizations (PDBe, PDBj, RCSB PDB, and BMRB). The PDB is a key in areas of structural biology, such as structural genomics. Most major scientific journals and some funding agencies now require scientists to submit their structure data to the PDB. Many other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
