We consider a modified Schrödinger equation wherein the electron-electron repulsion terms r_ij⁻¹ are approximated by truncated one-particle resolutions. Numerical results for the He atom and H₂ molecule at the Hartree–Fock, second-order Møller–Plesset, and configuration interaction levels show that the solutions of the resulting reduced-rank Schrödinger equations converge rapidly, and that even low-rank approximations can yield energies with chemical accuracy.