The Gutzwiller trace is about
$$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)l_{p}) $$
and $ l_{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. $$ H=p^{2}+V(x) $$