For the class of ‘‘heliumlike’’ Hamiltonians,H=− 1/2 ∇21− 1/2 ∇22+V(r1)+V(r2)+W(r12), there is a fortuitous choice of (attractive)Vand (repulsive)Wpotentials such that the system admits of exact analytic solution in both classical and quantum pictures. Specifically, harmonic attraction and inverse‐cube repulsion forces result in a soluble three‐body problem (with infinite nuclear mass). We derive the general classical electron trajectories and give a complete set of eigenfunctions of the Hamiltonian. We indicate how exact expectation values can be obtained and show that best fits to actual helium data require a nonzero repulsive coupling constant. We exhibit ans‐state basis subset of wave functions, suitable for application to general problems of atomic and chemical physics.