On the Existence of Solutions to Time-Dependent Hartree-Fock Equations

Abstract

where Xj=(x], xj, xj)ei2, Aj= ^ ( d / 3 x j ) 2 and Q(x V(x) are real functions such that V(x) = V(—x). If the system obeys the Fermi statistics, it is natural to treat (1.1) in the anti-symmetric subspace of L(R). Taking note of this anti-symmetry and using the variational principle, Dirac ([3], [4]) has derived the following time-dependent version of Hartree-Fock equation in order to obtain an approximate solution of (1.1) :