Could anyone please help a lowly 2nd year undergrad understand what the hamiltonian function of action(adsbygoogle = window.adsbygoogle || []).push({}); means!

[tex]W = \int_{t_0}^t \mathcal{L}\,dt[/tex]

Apparently Schrodinger used it along with the Hamilton-Jacobi equation to derive the Schrodinger equation so it's a pretty important part of quantum physics history.

According to wikipedia it's a function which takes the trajectory of a system and returns a real number. But this seems quite vague to me,whatis the significance of the scalar it outputs?

I've also looked in several books, but the mathematics of analytical mechanics is mind-boggling, I don't really have the time right now to fully digest the whole of the subject. The only definitions I've gotten from various book seem to be very vague and mathematical.

Thanks :)

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# What is Hamiltonian action?

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