Quantum operators — UPSC Physics Optional IFoS 2025 Paper II
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The raising (J_+) and lowering (J_-) operators are defined by J_+ = J_x + i J_y and J_- = J_x - i J_y. Show that– (i) [J_z, J_\pm] = \pm \hbar J_\pm (ii) J_+ J_- = J^2 - J_z^2 + \hbar J_z
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