I would like to get an answer or pointers to suitable material, on the following question:(adsbygoogle = window.adsbygoogle || []).push({});

I know that ∫|f(x)|^{2}dx is finite. Can we say that lim x→±∞ x*(d/dx)|f(x)|^{2}is zero? Are there any theorems about such limits with unknown functions that have some known properties? Basically this question arose from Griffith's introductory QM textbook which I started studying today (self study). f(x) is Ψ(x) and the author at page 16 takes the above limits to be zero "on the ground that Ψ goes to zero at ±∞". But it may go to zero asymptotically, and x goes to infinity, so we have an indeterminate form and we know only that the function's absolute value squared has a finite integral. I posted here, however, since I would like to get a more general answer on these types of limits and to be at least aware of the theory that deals with them.

Thanks in advance for your precious time people!

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# Limit of expression containing unknown function.

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