Maitra-Burke example of initial-state dependence in time-dependent density-functional theory

In a recent paper, Maitra and Burke [Phys. Rev. A 63, 042501 (2001); 64, 039901(E) (2001)] have given an interesting and instructive example that illustrates a specific feature of the time-dependent density-functional theory--the dependence of the reconstructed time-dependent potential not only on the electron density, but also on the initial state of the system. However, a concise form of its presentation by these authors is insufficient to reveal all its peculiarities. Our paper represents a very detailed study of this valuable example, intended to facilitate a better understanding and appreciation