  We have studied the ellipticity of quantum mechanical Hamiltonians, in
particular of the helium atom, in order to prove existence of a parametrix and
corresponding Green operator. The parametrix is considered in local
neighbourhoods of coalescence points of two particles. We introduce appropriate
hyperspherical coordinates where the singularities of the Coulomb potential are
considered as embedded edge/corner-type singularities. This shows that the
Hamiltonian can be written as an edge/corner degenerate differential operator
in a pseudo-differential operator algebra. In the edge degenerate case, we
prove the ellipticity of the Hamiltonian.
