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When I was going through canonical transformation I came across some equation like $$\dfrac{\partial^2 H}{\partial q \partial p} = \dfrac{\partial^2 H}{\partial p \partial q}$$ where $H$ is the Hamiltonian of a system and $q$ and $p$ are the coordinate and momentum. I know that partial differentiation is commutative when the function is of class $C^2$ . However I had no reason to believe that $H$ is so. So why does the relation hold? Can someone help me please?

Qmechanic
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    AFAIK, most rigorous formulations of Hamiltonian mechanics assume the Hamiltonian to be a smooth function on the phase space, so a function which is not even $C^2$ would not be a suitable candidate for a Hamiltonian. – J. Murray Mar 20 '18 at 15:09
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    Related: http://physics.stackexchange.com/q/1324/2451 and links therein. – Qmechanic Mar 20 '18 at 15:10

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