Bra-ket Notation in Quantum Mechanics

Bra Notation

In linear algebra both column vectors and row vectors are used. The Dirac notation provides a symbol called a bra. It represents a row vector. The bras correspond to the kets [html]|0>[/html] and [html]|a>[/html] are:

<0| = (1 0)
<1| = (0 1)

In a complex vector space V, every ket has a unique bra. The bras corresponding to a ket are obtained by taking the conjugate transpose of the ket (and vice versa). A bra [html]<u|[/html] acting on a vector v turns it into a complex number c, this can be written as:

<u|: v → c

Ket Notation

A vector v in a complex vector space V is denoted by a ket.

v>ε V

A ket is analogous to a column vector. Since the vector space is complex, all terms in a column vector are complex numbers.