Bra–ket notation

Bra–ket notation, Notation for quantum states.

In quantum mechanics, bra–ket notation, or Dirac notation, is ubiquitous. The notation uses the angle brackets, " ⟨ {\displaystyle \langle } " and " ⟩ {\displaystyle \rangle } ", and a vertical bar " | {\displaystyle |} ", to construct "bras" and "kets" . A ket looks like " | v ⟩ {\displaystyle |v\rangle } ". Mathematically it denotes a vector, v {\displaystyle {\boldsymbol {v}}} , in an abstract (complex) vector space V {\displaystyle V} , and physically it represents a state of some quantum system. A bra looks like " ⟨ f | {\displaystyle \langle f|} ", and mathematically it denotes a linear form f : V → C {\displaystyle f:V\to \mathbb {C} } , i.e.
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