We can then write the derivative as a function of its exponential and the identity operator.
pretty neat..
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This is why we call the derivative operator the "generator of translations".pic.twitter.com/VugmN68eZi
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Does this formula have any special meaning?
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In quantum mechanics it shows that the momentum operator is the generator of translations
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In the first equality it looks like you are Taylor expanding a derivative operator? What sort of theorem allows one to do it?
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There is no theorem, this is how the exponential of a linear operator is defined. That is, they are defined through the taylor expansion
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@robertghrist has a good discussion about this on a recent@myfavethm podcast and linking stability in continuous time and discrete timeThanks. Twitter will use this to make your timeline better. UndoUndo
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