97-599 Combescure M., Ralston J., Robert D.

A Proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition (48K, LATeX) Nov 28, 97

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Abstract. The Gutzwiller semiclassical trace formula links the eigenvalues of the Schrodinger operator H^ with the closed orbits of the corresponding classical mechanical system, associated with the Hamiltonian H, when the Planck constant is small (semiclassical regime). Gutzwiller gave a heuristic proof, using the Feynmann integral representation for the propagator of H^. Later on mathematicians gave rigorous proofs of this trace formula, under different settings, using the theory of Fourier Integral Operators and Lagrangian manifolds. Here we want to show how the use of coherent states (or gaussian beams) allows us to give a simple and direct proof.

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