Phy5645/Angular Momentum Problem 1

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

$=f(\phi )+{\frac {df(\phi )}{d\phi }}\Delta \phi +{\tfrac {1}{2}}{\frac {d^{2}f(\psi )}{d\phi ^{2}}}\left(\Delta \phi \right)^{2}+\cdots =f\left(\phi +\Delta \phi \right).$

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