Semiclassical quantization of the Liouville formulation of classical mechanics

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Abstract
A new method for the quantization of classical Hamiltonian systems is presented. This method is based upon the correspondence between the Liouville formulation of classical mechanics and the Liouville–von Neumann formulation of quantum mechanics. It does not distinguish between integrable and nonintegrable systems, and consequently, is equally applicable to both types of systems. Further, it treats the indistinguishability of identical particles correctly, and thus, the semiclassical eigenstates have the correct symmetry properties. Application of the method is illustrated by a series of examples. The results are in excellent agreement with quantum mechanics and represent an improvement over results obtained using the uniform semiclassical approximation.