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Delta Potential
In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds to a potential which is zero everywhere, except at a single point, where it takes an infinite value. This can be used to simulate situations where a particle is free to move in two regions of space with a barrier between the two regions. For example, an electron can move almost freely in a conducting material, but if two conducting surfaces are put close together, the interface between them acts as a barrier for the electron that can be approximated by a delta potential. The delta potential well is a limiting case of the finite potential well, which is obtained if one maintains the product of the width of the well and the potential constant while decreasing the well's width and increasing the potential. This article, for simplicity, only considers a one-dimensional potential well, but analysis could be expanded t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary ( macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves ( wave–particle duality); and there are lim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bound State
Bound or bounds may refer to: Mathematics * Bound variable * Upper and lower bounds, observed limits of mathematical functions Physics * Bound state, a particle that has a tendency to remain localized in one or more regions of space Geography *Bound Brook (Raritan River), a tributary of the Raritan River in New Jersey *Bound Brook, New Jersey, a borough in Somerset County People * Bound (surname) * Bounds (surname) Arts, entertainment, and media Films * ''Bound'' (1996 film), an American neo-noir film by the Wachowskis * ''Bound'' (2015 film), an American erotic thriller film by Jared Cohn * ''Bound'' (2018 film), a Nigerian romantic drama film by Frank Rajah Arase Television * "Bound" (''Fringe''), an episode of ''Fringe'' * "Bound" (''The Secret Circle''), an episode of ''The Secret Circle'' * "Bound" (''Star Trek: Enterprise''), an episode of ''Star Trek: Enterprise'' Other arts, entertainment, and media * ''Bound'' (video game), a PlayStation 4 game * "Bound", a so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Units
The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics and computational chemistry calculations. They are named after the physicist Douglas Hartree. By definition, the following four fundamental physical constants may each be expressed as the numeric value 1 multiplied by a coherent unit of this system: * Reduced Planck constant: \hbar, also known as the atomic unit of action * Elementary charge: e, also known as the atomic unit of charge * Bohr radius: a_0, also known as the atomic unit of length * Electron mass: m_\text, also known as the atomic unit of mass Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts. Defining constants Each unit in this system can be expressed as a product of powers of four physical constants without a multiplying constant. This makes it a coherent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen Molecule Ion
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 or m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dudley R
Dudley is a large market town and administrative centre in the county of West Midlands, England, southeast of Wolverhampton and northwest of Birmingham. Historically an exclave of Worcestershire, the town is the administrative centre of the Metropolitan Borough of Dudley; in 2011 it had a population of 79,379. The Metropolitan Borough, which includes the towns of Stourbridge and Halesowen, had a population of 312,900. In 2014 the borough council named Dudley as the capital of the Black Country. Originally a market town, Dudley was one of the birthplaces of the Industrial Revolution and grew into an industrial centre in the 19th century with its iron, coal, and limestone industries before their decline and the relocation of its commercial centre to the nearby Merry Hill Shopping Centre in the 1980s. Tourist attractions include Dudley Zoo and Castle, the 12th century priory ruins, and the Black Country Living Museum. History Early history Dudley has a history dating back ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen Atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe. In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary ( diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms). Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen (or any) atom can exist, contrary to the predictions of classical physics. Attempts to develop a the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian Of The Indicator
In mathematics, the Laplacian of the indicator of the domain ''D'' is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the ''surface'' of ''D''. It can be viewed as the ''surface delta prime function''. It is analogous to the second derivative of the Heaviside step function in one dimension. It can be obtained by letting the Laplace operator work on the indicator function of some domain ''D''. The Laplacian of the indicator can be thought of as having infinitely positive and negative values when evaluated very near the boundary of the domain ''D''. From a mathematical viewpoint, it is not strictly a function but a generalized function or measure. Similarly to the derivative of the Dirac delta function in one dimension, the Laplacian of the indicator only makes sense as a mathematical object when it appears under an integral sign; i.e. it is a distribution function. Just as in the formulation of distribution theory, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Potential Barrier (QM)
In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. The problem consists of solving the one-dimensional time-independent Schrödinger equation for a particle encountering a rectangular potential energy barrier. It is usually assumed, as here, that a free particle impinges on the barrier from the left. Although classically a particle behaving as a point mass would be reflected if its energy is less than a particle actually behaving as a matter wave has a non-zero probability of penetrating the barrier and continuing its travel as a wave on the other side. In classical wave-physics, this effect is known as evanescent wave coupling. The likelihood that the particle will pass through the barrier is given by the transmission coefficient, whereas the likelihood that it is reflected is given by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scanning Tunneling Microscope
A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most microscopes are built for use in ultra-high vacuum at temperatures approaching zero kelvin, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C. STM is based on the concept of quantum tunneling. When the tip is brought very near to the surface to be examined, a bias voltage applied between the two allows electrons to tunnel through the vacuum separating them. The resulting ''tunneling current'' is a function of the tip position, appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Mass (solid-state Physics)
In solid state physics, a particle's effective mass (often denoted m^*) is the mass that it ''seems'' to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material. In general, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated as a factor multiplying the rest mass of an electron, ''m'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm- meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter ( sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
