Equations de Hartree–Fock dependant du temps

Abstract

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.