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:

[html]<0| = (1 0) <1| = (0 1) [/html] 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]Ket Notation:

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

[html]|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.