Faster access than browser!
80 relations: Abuse of notation, Angular momentum diagrams (quantum mechanics), Angular momentum operator, Antilinear map, Associative property, Asterisk, Banach space, Basis (linear algebra), Borel functional calculus, Bracket, Change of basis, Complete metric space, Complex conjugate, Complex number, Conjugate transpose, Dirac delta function, Displacement (vector), Dot product, Dual space, Einstein notation, Energetic space, Energy, Expectation value (quantum mechanics), Finite-rank operator, Function composition, Functional analysis, Gelfand–Naimark–Segal construction, Hermann Grassmann, Hermitian adjoint, Hilbert space, Identical particles, Inner product space, Line (geometry), Linear algebra, Linear combination, Linear form, Linear map, Linear subspace, Mathematics, Matrix multiplication, Measurement in quantum mechanics, Momentum, N-slit interferometric equation, Norm (mathematics), Observable, Open Court Publishing Company, Orthonormal basis, Orthonormality, Outer product, Paul Dirac, ..., Plane wave, Position and momentum space, Probability amplitude, Projection (linear algebra), Quantum mechanics, Quantum number, Quantum state, Quantum superposition, Riesz representation theorem, Rigged Hilbert space, Ring (mathematics), Row and column vectors, Schrödinger picture, Self-adjoint, Self-adjoint operator, Spin (physics), Spin-½, Stationary state, T-symmetry, Tensor product, Time evolution, Topology, Transpose, Uncountable set, Unitary operator, Vector space, Velocity, Vertical bar, Wave function, Wave function collapse. Expand index (30 more) »
Abuse of notation
In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not formally correct but that seems likely to simplify the exposition or suggest the correct intuition (while being unlikely to introduce errors or cause confusion).
New!!: Bra–ket notation and Abuse of notation · See more »
Angular momentum diagrams (quantum mechanics)
In quantum mechanics and its applications to quantum many-particle systems, notably quantum chemistry, angular momentum diagrams, or more accurately from a mathematical viewpoint angular momentum graphs, are a diagrammatic method for representing angular momentum quantum states of a quantum system allowing calculations to be done symbolically.
New!!: Bra–ket notation and Angular momentum diagrams (quantum mechanics) · See more »
Angular momentum operator
In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum.
New!!: Bra–ket notation and Angular momentum operator · See more »
Antilinear map
In mathematics, a mapping f:V\to W from a complex vector space to another is said to be antilinear (or conjugate-linear) if for all a, \, b \, \in \mathbb and all x, \, y \, \in V, where \bar and \bar are the complex conjugates of a and b respectively.
New!!: Bra–ket notation and Antilinear map · See more »
Associative property
In mathematics, the associative property is a property of some binary operations.
New!!: Bra–ket notation and Associative property · See more »
Asterisk
An asterisk (*); from Late Latin asteriscus, from Ancient Greek ἀστερίσκος, asteriskos, "little star") is a typographical symbol or glyph. It is so called because it resembles a conventional image of a star. Computer scientists and mathematicians often vocalize it as star (as, for example, in the A* search algorithm or C*-algebra). In English, an asterisk is usually five-pointed in sans-serif typefaces, six-pointed in serif typefaces, and six- or eight-pointed when handwritten. It is often used to censor offensive words, and on the Internet, to indicate a correction to a previous message. The asterisk is derived from the need of the printers of family trees in feudal times for a symbol to indicate date of birth. The original shape was seven-armed, each arm like a teardrop shooting from the center. In computer science, the asterisk is commonly used as a wildcard character, or to denote pointers, repetition, or multiplication.
New!!: Bra–ket notation and Asterisk · See more »
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
New!!: Bra–ket notation and Banach space · See more »
Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
New!!: Bra–ket notation and Basis (linear algebra) · See more »
Borel functional calculus
In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope.
New!!: Bra–ket notation and Borel functional calculus · See more »
Bracket
A bracket is a tall punctuation mark typically used in matched pairs within text, to set apart or interject other text.
New!!: Bra–ket notation and Bracket · See more »
Change of basis
In linear algebra, a basis for a vector space of dimension n is a set of n vectors, called basis vectors, with the property that every vector in the space can be expressed as a unique linear combination of the basis vectors.
New!!: Bra–ket notation and Change of basis · See more »
Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
New!!: Bra–ket notation and Complete metric space · See more »
Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
New!!: Bra–ket notation and Complex conjugate · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: Bra–ket notation and Complex number · See more »
Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
New!!: Bra–ket notation and Conjugate transpose · See more »
Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
New!!: Bra–ket notation and Dirac delta function · See more »
Displacement (vector)
A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.
New!!: Bra–ket notation and Displacement (vector) · See more »
Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
New!!: Bra–ket notation and Dot product · See more »
Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
New!!: Bra–ket notation and Dual space · See more »
Einstein notation
In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.
New!!: Bra–ket notation and Einstein notation · See more »
Energetic space
In mathematics, more precisely in functional analysis, an energetic space is, intuitively, a subspace of a given real Hilbert space equipped with a new "energetic" inner product.
New!!: Bra–ket notation and Energetic space · See more »
Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
New!!: Bra–ket notation and Energy · See more »
Expectation value (quantum mechanics)
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment.
New!!: Bra–ket notation and Expectation value (quantum mechanics) · See more »
Finite-rank operator
In functional analysis, a branch of mathematics, a finite-rank operator is a bounded linear operator between Banach spaces whose range is finite-dimensional.
New!!: Bra–ket notation and Finite-rank operator · See more »
Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
New!!: Bra–ket notation and Function composition · See more »
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
New!!: Bra–ket notation and Functional analysis · See more »
Gelfand–Naimark–Segal construction
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called states).
New!!: Bra–ket notation and Gelfand–Naimark–Segal construction · See more »
Hermann Grassmann
Hermann Günther Grassmann (Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, known in his day as a linguist and now also as a mathematician.
New!!: Bra–ket notation and Hermann Grassmann · See more »
Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
New!!: Bra–ket notation and Hermitian adjoint · See more »
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
New!!: Bra–ket notation and Hilbert space · See more »
Identical particles
Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle.
New!!: Bra–ket notation and Identical particles · See more »
Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
New!!: Bra–ket notation and Inner product space · See more »
Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
New!!: Bra–ket notation and Line (geometry) · See more »
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
New!!: Bra–ket notation and Linear algebra · See more »
Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
New!!: Bra–ket notation and Linear combination · See more »
Linear form
In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.
New!!: Bra–ket notation and Linear form · See more »
Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
New!!: Bra–ket notation and Linear map · See more »
Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
New!!: Bra–ket notation and Linear subspace · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Bra–ket notation and Mathematics · See more »
Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
New!!: Bra–ket notation and Matrix multiplication · See more »
Measurement in quantum mechanics
The framework of quantum mechanics requires a careful definition of measurement.
New!!: Bra–ket notation and Measurement in quantum mechanics · See more »
Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
New!!: Bra–ket notation and Momentum · See more »
N-slit interferometric equation
Quantum mechanics was first applied to optics, and interference in particular, by Paul Dirac.
New!!: Bra–ket notation and N-slit interferometric equation · See more »
Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
New!!: Bra–ket notation and Norm (mathematics) · See more »
Observable
In physics, an observable is a dynamic variable that can be measured.
New!!: Bra–ket notation and Observable · See more »
Open Court Publishing Company
The Open Court Publishing Company is a publisher with offices in Chicago and La Salle, Illinois.
New!!: Bra–ket notation and Open Court Publishing Company · See more »
Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
New!!: Bra–ket notation and Orthonormal basis · See more »
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.
New!!: Bra–ket notation and Orthonormality · See more »
Outer product
In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.
New!!: Bra–ket notation and Outer product · See more »
Paul Dirac
Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.
New!!: Bra–ket notation and Paul Dirac · See more »
Plane wave
In the physics of wave propagation, a plane wave (also spelled planewave) is a wave whose wavefronts (surfaces of constant phase) are infinite parallel planes.
New!!: Bra–ket notation and Plane wave · See more »
Position and momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general could be any finite number of dimensions.
New!!: Bra–ket notation and Position and momentum space · See more »
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems.
New!!: Bra–ket notation and Probability amplitude · See more »
Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
New!!: Bra–ket notation and Projection (linear algebra) · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Bra–ket notation and Quantum mechanics · See more »
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of a quantum system.
New!!: Bra–ket notation and Quantum number · See more »
Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
New!!: Bra–ket notation and Quantum state · See more »
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics.
New!!: Bra–ket notation and Quantum superposition · See more »
Riesz representation theorem
There are several well-known theorems in functional analysis known as the Riesz representation theorem.
New!!: Bra–ket notation and Riesz representation theorem · See more »
Rigged Hilbert space
In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis.
New!!: Bra–ket notation and Rigged Hilbert space · See more »
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
New!!: Bra–ket notation and Ring (mathematics) · See more »
Row and column vectors
In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements, Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements Throughout, boldface is used for the row and column vectors.
New!!: Bra–ket notation and Row and column vectors · See more »
Schrödinger picture
In physics, the Schrödinger picture (also called the Schrödinger representation) is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are constant with respect to time.
New!!: Bra–ket notation and Schrödinger picture · See more »
Self-adjoint
In mathematics, an element x of a *-algebra is self-adjoint if x^*.
New!!: Bra–ket notation and Self-adjoint · See more »
Self-adjoint operator
In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.
New!!: Bra–ket notation and Self-adjoint operator · See more »
Spin (physics)
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
New!!: Bra–ket notation and Spin (physics) · See more »
Spin-½
In quantum mechanics, spin is an intrinsic property of all elementary particles.
New!!: Bra–ket notation and Spin-½ · See more »
Stationary state
A stationary state is a quantum state with all observables independent of time.
New!!: Bra–ket notation and Stationary state · See more »
T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal: T-symmetry can be shown to be equivalent to the conservation of entropy, by Noether's Theorem.
New!!: Bra–ket notation and T-symmetry · See more »
Tensor product
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
New!!: Bra–ket notation and Tensor product · See more »
Time evolution
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems).
New!!: Bra–ket notation and Time evolution · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Bra–ket notation and Topology · See more »
Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
New!!: Bra–ket notation and Transpose · See more »
Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
New!!: Bra–ket notation and Uncountable set · See more »
Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.
New!!: Bra–ket notation and Unitary operator · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: Bra–ket notation and Vector space · See more »
Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
New!!: Bra–ket notation and Velocity · See more »
Vertical bar
The vertical bar (|) is a computer character and glyph with various uses in mathematics, computing, and typography.
New!!: Bra–ket notation and Vertical bar · See more »
Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
New!!: Bra–ket notation and Wave function · See more »
Wave function collapse
In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation").
New!!: Bra–ket notation and Wave function collapse · See more »
Redirects here:
Bra and ket, Bra and ket vectors, Bra ket notation, Bra vector, Bra-ket, Bra-ket notation, Bra-ket notation for outer product, Bra.ket, Bracket notation, Braket, Braket notation, Bra–ket, Dirac notation, Dirac’s notation, Eigenket, Ket vector, Ketbra.
References
[1] https://en.wikipedia.org/wiki/Bra–ket_notation
