The three-body problem in the ground-state representation

The ground-state probability density of the 3B system is used to construct a classical potential, U, whose minimum coincides exactly with the ground-state energy. The spectrum of excited states may be approximately obtained by imposing quasiclassical quantization conditions over the classical motion on U. We show a nontrivial one dimensional model in which this quantization condition proves to be exact. For tridimensional problems, the small oscillation frequencies in states with total angular momentum L=0 are computed. These frequencies should represent an improvement over the frequencies of triatomic molecules computed using ordinary quasiclassics for the motion of the nuclei in the molecular term. By providing a semiclassical description of the first quantum excited states, the sketched approach raises some interesting questions such as, for example, the relevance (once again!) of classical chaos to Quantum Mechanics. (author). 22 refs