Phy5645/Angular Momentum Problem 1: Difference between revisions

Revision as of 22:27, 28 August 2013

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

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

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-:<math> \hat{R}_{\Delta \phi} f = \left[ \exp \left( \Delta \phi \frac{\partial}{\partial \phi} \right) \right] f </math>
+:<math> \hat{R}(\Delta\phi)f(\phi) = \left[ \exp \left( \Delta \phi \frac{\partial}{\partial \phi} \right) \right] f(\phi)</math>
-:<math> = 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).</math>
+:<math> = f(\phi) + \Delta \phi \frac{df(\phi)}{d\phi} + \tfrac{1}{2}\left(\Delta\phi\right)^2\frac{d^2 f(\psi)}{d\phi^2} + \cdots = f \left( \phi + \Delta \phi \right).</math>
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