| Abstract: | The time-dependent Hartree–Fock (TDHF ) equations are derived up to the second order when the system is perturbed by a monochromatic plane wave. The solutions of the equations are subjected to the orthonormalization conditions satisfied by the orbitals. In the equations, these conditions are expressed by the appearing of coefficients λ playing the part of Lagrangian multipliers. Relations between the coefficients λ are established. These relations are equivalent to the above-mentioned orthonormalization conditions. This equivalence enables us to substitute for the solution of an integrodifferential equation system subject to constraint conditions, that of a free system. The TDHF equations obtained determine the first- and second-order orbital perturbations, which no doubt verify the orthonormalization conditions. These orbitals can be used in the calculation, up to second order, of different nonlinear optical effects. |
