Corollary to the Hohenberg-Kohn Theorem

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In this paper we construct such a set of `degenerate' Hamiltonians H, which differ by an `intrinsic' constant but represent different physical systems yet possess the same ground state density.. Thus, although the proof of Hohenberg-Kohn (HK) theorem is independent of whether the constant C is additive or intrinsic, its applicability is restricted to excluding the case of the latter. This constitutes the corollary to the theorem.The corollary has also been extended to the time-dependent version of the HK theorem.