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Mathematics
Linear and Abstract Algebra
Rotate Functions with Derivatives: A Quantum Mechanics Homework
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[QUOTE="DrClaude, post: 6342002, member: 461323"] [URL='https://en.wikipedia.org/wiki/Translation_operator_(quantum_mechanics)#Momentum_as_generator_of_translations']Momentum is the generator of translation[/URL], so you can picture infinitesimal translations in x and y as a rotation in the xy plane. Note that the equation you get is only for infinitesimal rotations, and that the rotation operator around the z axis becomes ##e^{- i \hat{L}_z \varphi / \hbar}## for finite rotations, see [URL]https://en.wikipedia.org/wiki/Rotation_operator_(quantum_mechanics)[/URL] [/QUOTE]
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Rotate Functions with Derivatives: A Quantum Mechanics Homework
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