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Why is $L^2$ norm of the gradient called kinetic energy?
I'm reading Lieb-Loss's book 'Analysis', chapter 7. The authors refer to the following integral:
$$\tag{1} \lVert \nabla f\rVert_2^2=\int_{\Omega}\lvert \nabla f(x)\rvert^2\, d^nx $$
as the kinetic ...
