Calculating Length of Closed Orbits: Gutzwiller Formula & Hamiltonian Systems"

zetafunction
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given a Hamiltonian H=p^2 + V(x) how can you calculate the length of the closed orbits ? , i mean in gutzwiller formula you must perform a summation over the length of the closed orbits to calculate density of states g(E) but how can you know what the lenghts are ?? .. of course for Harmonic Oscillator orbits are circles so we can calculate their length but how about for other Hamiltonian systems ?
 
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The Gutzwiller formula is semi-classical. It uses classical periodic orbits.
 

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