A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition

Details A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition

1998-07-07

arxiv.org/abs/math-ph/9807005v1

Physics

Mathematical Physics

17 pages, LaTeX, available on http://qcd.th.u-psud.fr

Scientific paper

10.1007/s002200050591

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.

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