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Born–von Karman Boundary Condition
Born–von Karman boundary conditions are periodic boundary conditions which impose the restriction that a wave function must be periodic on a certain Bravais lattice. Named after Max Born and Theodore von Kármán, this condition is often applied in solid state physics to model an ideal crystal. Born and von Kármán published a series of articles in 1912 and 1913 that presented one of the first theories of specific heat of solids based on the crystalline hypothesis and included these boundary conditions. The condition can be stated as : \psi(\mathbf+N_i \mathbf_i)=\psi(\mathbf), \, where ''i'' runs over the dimensions of the Bravais lattice, the a''i'' are the primitive vectors of the lattice, and the ''Ni'' are integers (assuming the lattice has ''N'' cells where ''N=N1N2N3''). This definition can be used to show that : \psi(\mathbf+\mathbf)=\psi(\mathbf) for any lattice translation vector T such that: : \mathbf = \sum_i N_i \mathbf_i. Note, however, the Born– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Boundary Conditions
Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a ''unit cell''. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a ''world map'' of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (Compactification (mathematics), compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called ''images''. During the simulation, only the properties of the original simulation box need to be recorded and propaga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Band Structure
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ''forbidden bands''). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). Why bands and band gaps occur The formation of electronic bands and band gaps can be illustrated with two complementary models for electrons in solids. The first one is the nearly free electron model, in which the electrons are assumed to move almost freely within the material. In this model, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reviews Of Modern Physics
''Reviews of Modern Physics'' (often abbreviated RMP) is a quarterly Peer review, peer-reviewed scientific journal published by the American Physical Society. It was established in 1929 and the current editor-in-chief is Michael Thoennessen. The journal publishes review articles, usually by established researchers, on all aspects of physics and related fields. The reviews are usually accessible to non-specialists and serve as introductory material to graduate students, which survey recent work, discuss key problems to be solved and provide perspectives toward the end. The journal has published several historically significant papers on quantum foundations, as well as the development of the Standard Model of particle physics. References External links * Academic journals established in 1929 Physics review journals Quarterly journals English-language journals American Physical Society academic journals {{physics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holt, Rinehart And Winston
Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in high schools. The Holt name is derived from that of U.S. publisher Henry Holt (1840–1926), co-founder of the earliest ancestor business, but Holt McDougal is distinct from contemporary Henry Holt and Company, which claims the history from 1866. The companies publish different kinds of books. History Holt, Rinehart and Winston (HRW) was created in March 1960 by the merger of Henry Holt and Company of New York City (established 1866 as Leypoldt and Holt); Rinehart & Company of New York, descendant of Farrar & Rinehart (est. 1929); and the John C. Winston Company of Philadelphia (est. 1884). ''The Wall Street Journal'' reported on March 1, 1960, that Holt stockholders had approved the merger, last of the three approvals. "Henry Holt is the surviving concern, but will be known as Holt, Rinehart, Winston, Inc.""Henry Holt Merger". ''The Wall St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bloch's Theorem
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the Swiss physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where \mathbf is position, \psi is the wave function, u is a periodic function with the same periodicity as the crystal, the wave vector \mathbf is the crystal momentum vector, e is Euler's number, and i is the imaginary unit. Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. The description of electrons in terms of Bloch functions, termed Bloch electrons (or less often ''Bloch Waves''), underlies the concept of electronic band structures. These eigenstates are written with subscripts as \psi_, where n is a discrete index, called the band index, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple release of energy by objects to the realization of abilities in people. The philosopher Aristotle incorporated this concept into his theory of potentiality and actuality (in Greek, ''dynamis'' and ''energeia''), translated into Latin as ''potentia'' and ''actualitas'' (earlier also ''possibilitas'' and ''efficacia''). a pair of closely connected principles which he used to analyze motion, causality, ethics, and physiology in his ''Physics'', ''Metaphysics'', ''Nicomachean Ethics'', and '' De Anima'', which is about the human psyche. That which is potential can theoretically be made actual by taking the right action; for example, a boulder on the edge of a cliff has potential to fall that could be actualized by pushing it over the edge. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation, propagating wave. Diffraction is the same physical effect as Wave interference, interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660 in science, 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic pattern is most pronounced when a wave from a Coherence (physics), coherent source (such as a laser) encounters a slit/aperture tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physikalische Zeitschrift
''Physikalische Zeitschrift'' (English: ''Physical Journal'') was a German scientific journal of physics published from 1899 to 1945 by S. Hirzel Verlag. In 1924, it merged with ''Jahrbuch der Radioaktivität und Elektronik''. From 1944 onwards, the journal published the ''Reichsberichte für Physik'' (English: ''Third Reich, Reich Reports for Physics''). Several publications of great historical significance have been published in it, such as Albert Einstein's "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" (''On the Development of Our Views Concerning the Nature and Constitution of Radiation'') and Carl Friedrich von Weizsäcker, Carl von Weizsäcker's work on the CNO cycle, source of energy in stars. During its life, it was edited by several prominent physicists, such as Peter Debye. Towards the end of its life, it was considered to represent "the more conservative elements within the German physics community", alongside ''Annalen ... [...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] |
