I see in descriptions of the "old quantum theory", action formulated as(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\oint_{H(p,q)=E} p \dot{x} dt[/itex]

I'm struggling to see how that is equivalent to

[itex]\int \mathcal{L} dt[/itex], which I thought was the usual definition of action.

I know [itex]\mathcal{H}[/itex] is constructed so that [itex]p\dot{x} = \mathcal{H} + \mathcal{L}[/itex], but using that gives me an extra

[itex]\oint_{H(p,q)=E} \mathcal{H} dt = E \times T[/itex],

where T is the period of motion. Where am I going wrong?

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# Need help seeing that phase-space area is action

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