Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

Bra–ket notation

+ Save concept

In quantum mechanics, bra–ket notation is a standard notation for describing quantum states. [1]

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 »

Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: Bra–ket notation and Christmas · See more »

Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: Bra–ket notation and Christmas and holiday season · See more »

Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: Bra–ket notation and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: Bra–ket notation and Christmas traditions · 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 »

New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: Bra–ket notation and New Year · See more »

New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: Bra–ket notation and New Year's Day · See more »

New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: Bra–ket notation and New Year's Eve · 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 »

2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: Bra–ket notation and 2018 · See more »

2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: Bra–ket notation and 2019 · 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

OutgoingIncoming
Hey! We are on Facebook now! »