  The Gutzwiller semiclassical trace formula links the eigenvalues of the
Scrodinger 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
Feynman 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.
