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\begin{eqnarray}
|\alpha|=\cos{\theta\over2}\qquad|\beta|=\sin{\theta\over2},&&\qquad
0\le\theta\le n\label{eq04}\\
e^{-i\phi}={\alpha\over|\alpha|}.&&\qquad0\le\phi<2\pi\label{eq05}
\end{eqnarray}
\begin{align}
Orthonormal property \innerproduct{m}{n} = \delta_{mn}
Completeness property \sum_n \ket{n}\bra{n} = \hat{I},
\end{align}
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