## Tuesday Seminar of Analysis

Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

### 2010/07/13

17:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
[ Abstract ]
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.