We examine an interesting one‐dimensional problem involving two particles in an external field for which the Hartree equation can be solved analytically when both particles are in the same space orbital. The problem has close similarities to the three‐dimensional problem for the helium atom, although the external potential and the interaction potential are taken to be Dirac δ functions. The δ functions share an identical virial theorem with Coulomb potentials but are otherwise very different. The similarities of results in the two cases nevertheless extend to eigenvalues and wave functions. Some interesting generalizations are considered, including the one‐dimensional analog of the hydrogen molecule problem. These models and their solutions should prove useful as an introduction to the Hartree method for atomic and molecular physicists and chemists.