In QM and QFT, I have seen some equations where they have just the derivative and/or the gradient without specifying what it is acting on.
Taken from wiki.
This does not make sense to me since I learned that gradients and derivatives can only act on functions and not exist by themselves (unless they are vector components). This seems to be going against the grain of what I learned.
Can someone please help me understand how can we just put a derivative without specifying what it is acting on?