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Semiclassical trace formulae using coherent states. (English) Zbl 1033.81050

The authors use coherent states to obtain semiclassical trace formulae which include those previously obtained by Gutzwiller, relating the density of states of a quantum system to periodic orbits of the corresponding classical Hamiltonian. The method proposed by the authors, based on the remark that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator, improves the original proof of the trace formula done by Gutzwiller.

MSC:

81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81R30 Coherent states
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
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