Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page