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Bra–ket notation was created by Paul Dirac in his 1939 publication A New Notation for Quantum Mechanics. The notation was introduced as an easier way to write quantum mechanical expressions. [ 1 ] The name comes from the English word "bracket".
Dirac notation Synonymous to "bra–ket notation". Hilbert space Given a system, the possible pure state can be represented as a vector in a Hilbert space. Each ray (vectors differ by phase and magnitude only) in the corresponding Hilbert space represent a state. [nb 1] Ket
In some European countries, the notation [, [is also used for this, and wherever comma is used as decimal separator, semicolon might be used as a separator to avoid ambiguity (e.g., (;)). [ 6 ] The endpoint adjoining the square bracket is known as closed , while the endpoint adjoining the parenthesis is known as open .
A more complicated case is given (in bra–ket notation) by the singlet state, which exemplifies quantum entanglement: | = (| | ), which involves superposition of joint spin states for two particles with spin 1/2. The singlet state satisfies the property that if the particles' spins are measured along the same direction then either the spin of ...
Writing for an eigenstate and for the corresponding observed value, any arbitrary state of the quantum system can be expressed as a vector using bra–ket notation: | = | . The kets { | ϕ i } {\displaystyle \{|\phi _{i}\rangle \}} specify the different available quantum "alternatives", i.e., particular quantum states.
The notational conventions used in this article are as follows. Boldface indicates vectors, four vectors, matrices, and vectorial operators, while quantum states use bra–ket notation. Wide hats are for operators, narrow hats are for unit vectors (including their components in tensor index notation).
This is known as Dirac notation or bra–ket notation, to note vectors from the dual spaces of the Bra A| and the Ket |B . But there are other notations used. In continuum mechanics , chevrons may be used as Macaulay brackets .
In bra–ket notation the above can be written; ^ ... The definition of a Hermitian operator is: [1] ^ = ^ ...