Quantum operators — UPSC Physics Optional CSE 2012 Paper II

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Given that $\sigma_x,\sigma_y,\sigma_z$ are Pauli spin operators, prove the following relationships:

(i) $\sin(\sigma_x\varphi)=\sigma_x\sin\varphi$

(ii) $\cos(\sigma_z\varphi)=\cos\varphi$

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