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The Gutzwiller trace formula links the eigenvalues of the Schrödinger operator H as Planck's constant goes to zero (the semiclassical régime) with the closed orbits of the corresponding classical mechanical system. Gutzwiller gave a heuristic proof of this trace formula, using the Feynman integral representation for the propagator of H. Later, using the theory of Fourier integral operators, mathematicians gave rigorous proofs of the formula in various settings. Here we show how the use of coherent states allows us to give a simple and direct proof.

We derive three results on the inverse problem of determining the Lamé parameters λ(x) and μ(x) for an isotropic elastic body from its Dirichlet-to-Neumann map.

In this article we consider the Schrδdinger operator in R n ,n ^ 3, with electric and magnetic potentials which decay exponentially as \x\ -> oo. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field.