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Dirac Notation:

The standard notation for a state vector is a ket vector |$ \Psi$$ \rangle$. For example, a vector in $ \Real^{{3}}_{}$ with basis $ \hat{{i}}$,$ \hat{{j}}$,$ \hat{{k}}$ is typically written as

$\displaystyle \vec{{v}} $ = a$\displaystyle \hat{{i}}$ + b$\displaystyle \hat{{j}}$ + c$\displaystyle \hat{{k}}$ = (a, b, c)T.

In Dirac notation, it would be written as

| v$\displaystyle \rangle$ = a| i$\displaystyle \rangle$ + b| j$\displaystyle \rangle$ + c| k$\displaystyle \rangle$ = (a, b, c)T.

The term ket and this notation come from the physicist Paul Dirac who wanted a concise way of writing formulas involving row and column vectors. He referred to row vectors as bra vectors represented as $ \langle$y|. The inner product of a bra and a ket vector is written $ \langle$y| x$ \rangle$, and is called a bracket [18].


next up previous contents
Next: Superposition Up: State Vectors and Dirac Previous: State Vectors:   Contents
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