Semiclassical quantization and extraction of eigenfunctions using arbitrary trajectories

We present in this paper a coordinate independent semiclassical quantization method. We demonstrate that in order to extract accurate eigenvalues and eigenfunctions the trajectory does not necessarily have to reside on the quantizing torus, rather, one can use information obtained on arbitrary tori. Because the method is coordinate independent, no difficulty is encountered in quantizing within classical resonance zones. Furthermore, nearby eigenstates and eigenvalues (nearby in action space) may be extracted from the same trajectory—this is especially convenient when the density of states becomes large.