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In computational algebra, the Cantor–Zassenhaus algorithm is a method for factoring polynomials over finite fields (also called Galois fields).
The algorithm consists mainly of exponentiation and polynomial GCD computations. It was invented by David G. Cantor and Hans Zassenhaus in 1981.
It is arguably the dominant alg... | Wikipedia/Cantor–Zassenhaus_algorithm |
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called hash values, hash codes, (hash/message) digests, or simply hashes. The values are usually used... | Wikipedia/Hash_function |
The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra.
Buchberger's algorithm f... | Wikipedia/Knuth–Bendix_completion_algorithm |
Fermat (named after Pierre de Fermat) is a computer algebra system developed by Prof. Robert H. Lewis of Fordham University. It can work on integers (of arbitrary size), rational numbers, real numbers, complex numbers, modular numbers, finite field elements, multivariable polynomials, rational functions, or polynomials... | Wikipedia/Fermat_(computer_algebra_system) |
Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma. It runs on Unix-like operating systems, as well as Windows.
== Introduction ==
Magma is produced and distributed by the Computational Algebra Group with... | Wikipedia/Magma_(computer_algebra_system) |
Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy.
== History ==
Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Griesmer at the reques... | Wikipedia/Axiom_(computer_algebra_system) |
Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations. It provides many useful specialized functions and equations for the solution of thermodynamics and heat transfer problems, making it a useful and widely used program for mechanical engin... | Wikipedia/Engineering_Equation_Solver |
GAP (Groups, Algorithms and Programming) is an open source computer algebra system for computational discrete algebra with particular emphasis on computational group theory.
== History ==
GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to ... | Wikipedia/GAP_(computer_algebra_system) |
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally.
In addition to the integrator devices, the machine used an epicycl... | Wikipedia/Differential_analyser |
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of... | Wikipedia/Irrational_function |
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring
K
[
x
1
... | Wikipedia/Multivariate_division_algorithm |
Derive was a computer algebra system, developed as a successor to muMATH by the Soft Warehouse in Honolulu, Hawaii, now owned by Texas Instruments. Derive was implemented in muLISP, also by Soft Warehouse. The first release was in 1988 for DOS. It was discontinued on June 29, 2007, in favor of the TI-Nspire CAS. The fi... | Wikipedia/Derive_(computer_algebra_system) |
In mathematics, Gosper's algorithm, due to Bill Gosper, is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms. That is: suppose one has a(1) + ... + a(n) = S(n) − S(0), where S(n) is a hypergeometric term (i.e., S(n + 1)/S(n) is a rational function of n); then necessarily a(n)... | Wikipedia/Gosper's_algorithm |
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of... | Wikipedia/Model_checker |
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms i... | Wikipedia/Algebra_(ring_theory) |
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is
[
... | Wikipedia/Scalar_transformation |
In mathematics, a Lie algebra
g
{\displaystyle {\mathfrak {g}}}
is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra of the Lie algebra
g
... | Wikipedia/Derived_algebra |
In mathematics, the special linear Lie algebra of order
n
{\displaystyle n}
over a field
F
{\displaystyle F}
, denoted
s
l
... | Wikipedia/Special_linear_Lie_algebra |
In linear algebra, an eigenvector ( EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector
v
{\displaystyle \mathbf {v} }
of a linear transformation
... | Wikipedia/Algebraic_multiplicity |
In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which ... | Wikipedia/Direct_sum_of_Lie_algebras |
In mathematics, a Lie algebra (pronounced LEE) is a vector space
g
{\displaystyle {\mathfrak {g}}}
together with an operation called the Lie bracket, an alternating bilinear map
g
... | Wikipedia/Lie_algebras |
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform (with sign reversal) of the probability density func... | Wikipedia/Characteristic_function_(probability_theory) |
This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see:
Tensor
Tensor (intrinsic definition)
Application of tensor theory in engineering science
For some history of the abstract theory see also multilinear algebra.
== Classical notation ==
Ricci calculus
The earliest... | Wikipedia/Tensor_notation |
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential of a variable
x
{\displaystyle x}
is denoted
exp
x
{\di... | Wikipedia/Complex_exponential_function |
Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems.
Theoretical aspects of data management include, among other areas, the foundations of query languages, computational complexity and expressive power of queries, ... | Wikipedia/Database_theory |
In commutative algebra, the constructible topology on the spectrum
Spec
(
A
)
{\displaystyle \operatorname {Spec} (A)}
of a commutative ring
A
{\displaystyle A}
is a topology where each closed set i... | Wikipedia/Constructible_topology |
In the mathematical field of model theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted in the proof of Morley's categoricity theorem and were extensively studied as part of Saharon Shelah's classification theory, which showed a dichotomy t... | Wikipedia/Stable_theory |
In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone.... | Wikipedia/Stone's_representation_theorem_for_Boolean_algebras |
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes... | Wikipedia/Formal_language_theory |
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.... | Wikipedia/Mordell-Lang_conjecture |
In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem (proven in several different ways).
The conjecture concerns itself with a characterization of the Zariski closur... | Wikipedia/André–Oort_conjecture |
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.... | Wikipedia/Mordell–Lang_conjecture |
In model theory—a branch of mathematical logic—a minimal structure is an infinite one-sorted structure such that every subset of its domain that is definable with parameters is either finite or cofinite. A strongly minimal theory is a complete theory all models of which are minimal. A strongly minimal structure is a st... | Wikipedia/Strongly_minimal_theory |
In model theory, a branch of mathematical logic, a complete theory T is said to satisfy NIP ("not the independence property") if none of its formulae satisfy the independence property—that is, if none of its formulae can pick out any given subset of an arbitrarily large finite set.
== Definition ==
Let T be a complet... | Wikipedia/NIP_(model_theory) |
Model-theoretic grammars, also known as constraint-based grammars, contrast with generative grammars in the way they define sets of sentences: they state constraints on syntactic structure rather than providing operations for generating syntactic objects. A generative grammar provides a set of operations such as rewrit... | Wikipedia/Model-theoretic_grammar |
This page is about the concept in mathematical logic. For the concepts in sociology, see Institutional theory and Institutional logic.
In mathematical logic, institutional model theory generalizes a large portion of first-order model theory to an arbitrary logical system.
== Overview ==
The notion of "logical system... | Wikipedia/Institutional_model_theory |
In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism. Omega-categoricity is the special case κ =
ℵ
0
{\displaystyle \aleph _{0}}
= ω of κ-categoric... | Wikipedia/Omega-categorical_theory |
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding.
Equivalently, every first-order formula is equivalent to a universal formula.
This notion was introduced by Abraham Robinson.
== Model companion and model completion ==
A companion of a theory... | Wikipedia/Model_completion |
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding.
Equivalently, every first-order formula is equivalent to a universal formula.
This notion was introduced by Abraham Robinson.
== Model companion and model completion ==
A companion of a theory... | Wikipedia/Model-complete |
Computable model theory is a branch of model theory which deals with questions of computability as they apply to model-theoretical structures.
Computable model theory introduces the ideas of computable and decidable models and theories and one of the basic problems is discovering whether or not computable or decidable... | Wikipedia/Computable_model_theory |
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding.
Equivalently, every first-order formula is equivalent to a universal formula.
This notion was introduced by Abraham Robinson.
== Model companion and model completion ==
A companion of a theory... | Wikipedia/Model_companion |
In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are mainly studied in real algebraic geometry... | Wikipedia/Semialgebraic_sets |
In mathematical logic, and more specifically in model theory, an infinite structure (M,<,...) that is totally ordered by < is called an o-minimal structure if and only if every definable subset X ⊆ M (with parameters taken from M) is a finite union of intervals and points.
O-minimality can be regarded as a weak form of... | Wikipedia/O-minimal_theory |
In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by
c
{\displaystyle {\mathfrak {c}}}
. Georg Cantor proved that the cardinality
... | Wikipedia/Continuum_(set_theory) |
In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models.
Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. The starting point fo... | Wikipedia/Abstract_model_theory |
The term transformation theory refers to a procedure and a "picture" used by Paul Dirac in his early formulation of quantum theory, from around 1927.
This "transformation" idea refers to the changes a quantum state undergoes in the course of time, whereby its vector "moves" between "positions" or "orientations" in its ... | Wikipedia/Transformation_theory_(quantum_mechanics) |
In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that certain pairs of complementary properties cannot all be observed or measured simultaneously. For example, position and momentum, frequency and ... | Wikipedia/Complementarity_(physics) |
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... | Wikipedia/Modern_Quantum_Mechanics |
Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a machine able to perform quantum circui... | Wikipedia/Quantum_network |
Quantum Theory: Concepts and Methods is a 1993 quantum physics textbook by Israeli physicist Asher Peres. Well-regarded among the physics community, it is known for unconventional choices of topics to include.
== Contents ==
In his preface, Peres summarized his goals as follows:
The purpose of this book is to clarif... | Wikipedia/Quantum_Theory:_Concepts_and_Methods |
Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physi... | Wikipedia/Symmetry_in_quantum_mechanics |
Quantization (in British English quantisation) is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing quantum mechanics from classical mechanics. A generalization involving infinite degrees o... | Wikipedia/Quantization_(physics) |
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These models attempt to account for the probabilistic features of quantum mechanics via the mechanism of underlying but inaccessible variables, with the additional requirement... | Wikipedia/Local_hidden-variable_theory |
Physics World is the membership magazine of the Institute of Physics, one of the largest physical societies in the world. It is an international monthly magazine covering all areas of physics, pure and applied, and is aimed at physicists in research, industry, physics outreach, and education worldwide.
== Overview ==... | Wikipedia/Physics_World |
In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables.
The mathematical formulation of quantum mechanics assumes that the state of a system prior to measurement is indeterminate; quan... | Wikipedia/Hidden_variable_theory |
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved sc... | Wikipedia/Regularization_(physics) |
Atomic theory is the scientific theory that matter is composed of particles called atoms. The definition of the word "atom" has changed over the years in response to scientific discoveries. Initially, it referred to a hypothetical concept of there being some fundamental particle of matter, too small to be seen by the n... | Wikipedia/Atomic_theory |
Objective-collapse theories, also known spontaneous collapse models or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes... | Wikipedia/Objective-collapse_theory |
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreti... | Wikipedia/Matrix_mechanics |
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the... | Wikipedia/Wave_theory_of_light |
A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under contr... | Wikipedia/Scientific_theory |
Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still use... | Wikipedia/Introduction_to_quantum_mechanics |
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states c... | Wikipedia/Degenerate_energy_levels |
In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own antiparticle. Particles corresponding to this equation are termed Majorana particles, although that term now has a more... | Wikipedia/Majorana_equation |
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air,... | Wikipedia/Non-linear_dynamics |
In various interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation and is ... | Wikipedia/Wave_function_collapse |
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution, which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in... | Wikipedia/Quantum_cryptography |
In physics, quantum dynamics is the quantum version of classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of quantum mechanics. Quantum dynamics is relevant for burgeoning fields, such as quantum computing and atomic optics.
I... | Wikipedia/Quantum_dynamics |
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory st... | Wikipedia/Chaotic_systems |
In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three possible types of elementary fermions, the other two being the Dirac and t... | Wikipedia/Weyl_equation |
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is ... | Wikipedia/Dirac_equation |
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or mo... | Wikipedia/Energy_level |
QED: The Strange Theory of Light and Matter is an adaptation for the general reader of four lectures on quantum electrodynamics (QED) published in 1985 by American physicist and Nobel laureate Richard Feynman.
QED was designed to be a popular science book, written in a witty style, and containing just enough quantum-me... | Wikipedia/QED:_The_Strange_Theory_of_Light_and_Matter |
In mathematical physics, the WKB approximation or WKB method is a technique for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wave function is recast as an exponential function, ... | Wikipedia/WKB_approximation |
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a r... | Wikipedia/Quantum_neural_network |
The timeline of quantum mechanics is a list of key events in the history of quantum mechanics, quantum field theories and quantum chemistry.
The initiation of quantum science occurred in 1900, originating from the problem of the oscillator beginning during the mid-19th century.
== 19th century ==
1801 – Thomas Young... | Wikipedia/Timeline_of_quantum_mechanics |
Coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere.: 286 Wave sources are not strictly monochromatic: they may be partly coherent.
When interfering, two waves add together to create a wave of greater amplitude than either one (constructive inter... | Wikipedia/Coherence_(physics) |
Nanotechnology is the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm). At this scale, commonly known as the nanoscale, surface area and quantum mechanical effects become important in describing properties of matter. This definition of nanotechnology includes all types of research ... | Wikipedia/Quantum_nanoscience |
In theoretical physics, the Rarita–Schwinger equation is the
relativistic field equation of spin-3/2 fermions in a four-dimensional flat spacetime. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941.
In modern notation it can be w... | Wikipedia/Rarita–Schwinger_equation |
In various interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation and is ... | Wikipedia/Collapse_of_the_wavefunction |
Energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted ... | Wikipedia/Total_energy |
In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables.
The mathematical formulation of quantum mechanics assumes that the state of a system prior to measurement is indeterminate; quan... | Wikipedia/Hidden-variable_theory |
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear model, it supplanted the plum pudding model of J. J. Thomson only to be replaced by the quantum atomic m... | Wikipedia/Bohr_model |
The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small to be seen with a microscope, in constant, random motion. These particles are... | Wikipedia/Kinetic_theory_of_gases |
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is named after Oskar Klein and Walter Gordon. It is second-order in space and time and manifestly Lorentz-covariant. It is a differential equation versi... | Wikipedia/Klein–Gordon_equation |
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being relational, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded u... | Wikipedia/Relational_quantum_mechanics |
Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories.: 148 Just as the Lindblad master equation provides a quan... | Wikipedia/Quantum_stochastic_calculus |
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments. However, there exist a number of contending sc... | Wikipedia/Interpretations_of_quantum_mechanics |
A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a hypothetical singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe.: 6 Finding a theory of everything is one of the major unsolved ... | Wikipedia/Theory_of_Everything |
In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-1/2 particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used whe... | Wikipedia/Pauli_equation |
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is
1
2
m
... | Wikipedia/Kinetic_energy |
Quantum physics is a branch of modern physics in which energy and matter are described at their most fundamental level, that of energy quanta, elementary particles, and quantum fields. Quantum physics encompasses any discipline concerned with systems that exhibit notable quantum-mechanical effects, where waves have pro... | Wikipedia/Applications_of_quantum_mechanics |
In physics, relativistic quantum mechanics (RQM) is any Poincaré-covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high-energy... | Wikipedia/Relativistic_quantum_mechanics |
In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum mechanics, while generalizations of or departu... | Wikipedia/Unitarity_(physics) |
Physics Physique Физика, also known as various punctuations of Physics, Physique, Fizika, and as Physics for short, was a scientific journal published from 1964 through 1968. Founded by Philip Warren Anderson and Bernd T. Matthias, who were inspired by wide-circulation literary magazines like Harper's, the journal's or... | Wikipedia/Physics_Physique_Fizika |
Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrat... | Wikipedia/Zero-point_energy |
Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect, Josephson ... | Wikipedia/Macroscopic_quantum_phenomena |
The de Broglie–Bohm theory is an interpretation of quantum mechanics which postulates that, in addition to the wavefunction, an actual configuration of particles exists, even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave functi... | Wikipedia/Bohmian_mechanics |
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often deno... | Wikipedia/Charge_(physics) |
The old quantum theory is a collection of results from the years 1900–1925, which predate modern quantum mechanics. The theory was never complete or self-consistent, but was instead a set of heuristic corrections to classical mechanics. The theory has come to be understood as the semi-classical approximation to modern ... | Wikipedia/Old_quantum_theory |
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