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- Bra–ket_notation abstract "In quantum mechanics, bra–ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics. It is so called because the inner product (or dot product on a complex vector space) of two states is denoted by a <bra|ket>,,consisting of a left part, <φ|, called the bra /brɑː/, and a right part, |ψ>, called the ket /kɛt/. The notation was introduced in 1939 by Paul Dirac and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation [φ|ψ] for his inner products nearly 100 years previously.Bra–ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics—including a large portion of modern physics — is usually explained with the help of bra–ket notation. Part of the appeal of the notation is the abstract representation-independence it encodes, together with its versatility in producing a specific representation (e.g. x, or p, or eigenfunction base) without much ado, or excessive reliance on the nature of the linear spaces involved. The overlap expression ⟨φ|ψ⟩ is typically interpreted as the probability amplitude for the state ψ to collapse into the state ϕ.".
- Bra–ket_notation thumbnail Vector_components_bases_projection.svg?width=300.
- Bra–ket_notation wikiPageID "4542".
- Bra–ket_notation wikiPageRevisionID "605427035".
- Bra–ket_notation caption "Continuous components ψ of a complex vector = ∫dx ψ, which belongs to an uncountably infinite-dimensional Hilbert space; there are infinitely many x values and basis vectors .".
- Bra–ket_notation caption "Discrete components A'k of a complex vector = ∑k A'k, which belongs to a countably infinite-dimensional Hilbert space; there are countably infinitely many k values and basis vectors .".
- Bra–ket_notation footer "Components of complex vectors plotted against index number; discrete k and continuous x. Two particular components out of infinitely many are highlighted.".
- Bra–ket_notation image "Continuous complex vector components.svg".
- Bra–ket_notation image "Discrete complex vector components.svg".
- Bra–ket_notation width "225".
- Bra–ket_notation width "230".
- Bra–ket_notation subject Category:Information_theory.
- Bra–ket_notation subject Category:Linear_algebra.
- Bra–ket_notation subject Category:Mathematical_notation.
- Bra–ket_notation subject Category:Paul_Dirac.
- Bra–ket_notation subject Category:Quantum_information_science.
- Bra–ket_notation subject Category:Quantum_mechanics.
- Bra–ket_notation comment "In quantum mechanics, bra–ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics. It is so called because the inner product (or dot product on a complex vector space) of two states is denoted by a <bra|ket>,,consisting of a left part, <φ|, called the bra /brɑː/, and a right part, |ψ>, called the ket /kɛt/.".
- Bra–ket_notation label "Bra–ket notation".
- Bra–ket_notation label "Dirac-Notation".
- Bra–ket_notation label "Diracnotatie".
- Bra–ket_notation label "Notación bra-ket".
- Bra–ket_notation label "Notacja Diraca".
- Bra–ket_notation label "Notation bra-ket".
- Bra–ket_notation label "Notazione bra-ket".
- Bra–ket_notation label "Notação Bra-ket".
- Bra–ket_notation label "Бра и кет".
- Bra–ket_notation label "رمز براكيت".
- Bra–ket_notation label "ブラ-ケット記法".
- Bra–ket_notation label "狄拉克符号".
- Bra–ket_notation sameAs Bra%E2%80%93ket_notation.
- Bra–ket_notation sameAs Diracova_notace.
- Bra–ket_notation sameAs Dirac-Notation.
- Bra–ket_notation sameAs Συμβολισμός_Ντιράκ.
- Bra–ket_notation sameAs Notación_bra-ket.
- Bra–ket_notation sameAs Notation_bra-ket.
- Bra–ket_notation sameAs Notazione_bra-ket.
- Bra–ket_notation sameAs ブラ-ケット記法.
- Bra–ket_notation sameAs 브라-켓_표기법.
- Bra–ket_notation sameAs Diracnotatie.
- Bra–ket_notation sameAs Notacja_Diraca.
- Bra–ket_notation sameAs Notação_Bra-ket.
- Bra–ket_notation sameAs Q59090.
- Bra–ket_notation sameAs Q59090.
- Bra–ket_notation wasDerivedFrom Bra–ket_notation?oldid=605427035.
- Bra–ket_notation depiction Vector_components_bases_projection.svg.
