Phy5645/Angular Momentum Problem 1

${\hat {R}}_{\Delta \phi }f=\left[\exp \left(\Delta \phi {\frac {\partial }{\partial \phi }}\right)\right]f$

$=f(\phi )+\Delta \phi {\frac {\partial f}{\partial \phi }}+{\frac {\left(\Delta \phi \right)^{2}}{2}}{\frac {\partial ^{2}f}{\partial \phi ^{2}}}+\cdots =f\left(\phi +\Delta \phi \right).$

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