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The Gutzwiller semiclassical trace formula links the eigenvalues of theScrodinger operator ^H with the closed orbits of the corresponding classicalmechanical system, associated with the Hamiltonian H, when the Planck constantis small ("semiclassical regime"). Gutzwiller gave a heuristic proof, using theFeynman integral representation for the propagator of ^H. Later onmathematicians gave rigorous proofs of this trace formula, under differentsettings, using the theory of Fourier Integral Operators and Lagrangianmanifolds. Here we want to show how the use of coherent states (or gaussianbeams) allows us to give a simple and direct proof.

A Proof of the Gutzwiller Semiclassical Trace Formula Using Coherent States Decomposition