Periodic numerical solutions of the time-dependent Hartree-Fock equations

We propose a numerical algorithm for finding periodic solutions of the time-dependent Hartree-Fock equations. We show that this algorithm preserves the particle number and the total energy exactly. We demonstrate the method by calculating the periodic breathing mode of {sup 4}He. We discuss the generalization to more realistic cases, including multidimensional periodic modes. {copyright} {ital 1997} {ital The American Physical Society}