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The Gutzwiller trace is about

$$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$

and $ \ell_{p} $ are the length of the orbit.

However my question is, how can one derive the length of the orbit from the potential inside the quantum Hamiltonian. $$ H=p^{2}+V(x) $$.

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