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. 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,
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3419)
called the
bra , and a right part,
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=701)
, called the
ket . 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 for his inner products nearly 100 years earlier.