Classical-quantum correspondence in a helium-like system on conic sections

We present results of a study on the classical-quantum correspondence in a model of a three-body Coulomb system. The model simulates a helium atom, fo r which the motion of two electrons is restricted to move on coplanar ellip ses. Some of classical periodic orbits of this model system are found analy tically or numerically, including the well-known Wannier and Langmuir orbit s. These periodic orbits play an important role in quantum solutions in the sense that they scar the probability amplitude distributions of some of th e eigenfunctions of the system.