XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Carlos Villegas-Blas

On a limiting distribution eigenvalue theorem for perturbations of the hydrogen atom.

In this talk we describe a theorem on the distribution of eigenvalues of suitable perturbations of the hydrogen atom Hamiltonian in the semiclassical limit ($\hbar\tends{0}$). The perturbations are of the type $\epsilon{Q}$ with $\epsilon=O(\hbar)$ and Q a bounded multiplicative operator. The mentioned above limit is an integral over an $SO(4)$ invariant probability measure on the unit cotangent bundle of the 3-sphere and involves the Radon transform of the potential $Q$ along the Kepler orbits (including the collision ones) with a fixed energy $E=-1/2$. This is a joint work with Alejandro Uribe.