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In a discussion of the historical motivations for a move from calculus to operators, my QM book says...

"Many mathematicians were uncomfortable with the 'metaphysical implications' of a mathematics formulated in terms of infinitesimal quantities (like dx). This disquiet was the stimulus for the development of the operator calculus."

This is all fine and well, but I just don't see how the use of operators lets one escape the 'uncomfortable metaphysical implications' of the calculus. I mean, you're still doing the same thing to a function with the only difference (as far as I can tell) being that you use a far more concise notation to get the same job done.

How is operator calculus so fundamentally different than plain old calculus? I just cannot see the big difference between the two.

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# Curious statement about operators in my QM book?

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