Hylleraas representation

Accuracy of calculation has not been a problem for some time. For example, elaborate calculations based on many variational terms in a Hylleraas representation have been carried out by Bhatia and co-workers,3 and highly accurate complex-scaling calculations have been performed by Ho.4 A representation based on collective hyperspherical coordinates... 

A suitable representation of the helium wave function was taken to be the Hylleraas form... 

The precise connection with finite dimensional matrix formulas obtains simply from Lowdin s inner and outer projections [21, 22], see more below, or equivalently from the corresponding Hylleraas-Lippmann-Schwinger-type variational principles [24, 25]. For instance, if we restrict our operator representations to an n-dimensional linear manifold (orthonormal for simplicity) defined by... 

The ground state of helium is itself a rather special case as the wave function is relatively compact. It is thus not difficult to get a reasonable representation of this wave function with a rather modest, correlated basis set. Hylleraas[16]... 

---