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If $\vec{\alpha}$ is a vector $(\alpha_1,\alpha_2,\alpha_3)$, show that $$ (\vec{\alpha}\cdot\vec{\sigma})^2 = |\vec{\alpha}|^2$$ where \(|\alpha|=\sqrt{\alpha_1^2+\alpha_2^2+\alpha_3^2}\) Use this result and show that \[\exp(i\vec{\alpha}\cdot\vec{\sigma}) =
\cos{|\vec{\alpha}|} + i\vec{\alpha}\cdot\sigma \sin|\vec{\alpha}|\]
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4727:Diamond Point
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