Bra–ket notation

In quantum mechanics, bra–ket notation is a standard notation for describing quantum states. The notation uses angle brackets ("${\displaystyle \langle }$", and "${\displaystyle \rangle }$") and vertical bars ("${\displaystyle \mid }$"). It can also be used to denote abstract vectors and linear functionals in mathematics. In such terms, the scalar product, or action of a linear functional on a vector in a complex vector space, is denoted by

consisting of a left part,

called the bra /brɑː/, and a right part,

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