Subspace density of the first excited state for two harmonically interacting electrons with isotropic harmonic confinement

The subspace density and pair density at coincidence of the first excited state for two harmonically interacting electrons with antiparallel spins and isotropic harmonic confinement are calculated. It is shown that the total energy is uniquely determined by the value of the pair density at coincidence at r=0. A relationship between the energy and the subspace density at r=0 is derived.