In physics, this is why we call the derivative operator the "generator of translations"pic.twitter.com/iqJoydnylt
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(d/dx)^2 = d^2/dx^2 ??
Indeed, this is precisely what it means to square an operator. Think of matrices, M^2 just means apply M twice
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Your thought are correct but notations... it is a good reason to be mad for a mathematician. But of course no problem :)
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Right but this is common notation, even for mathematicians
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