Carlos VillegasBlas
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 3sphere 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.
