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22.5. QUESTIONS ON GENERAL PRINCIPLES OF TDDFT 177 178 CHAPTER 22. TIME-DEPENDENT DENSITY FUNCTIONAL THEORY
Bibliography
The original proof of the Runge-Gross theorem is in Density-functional theory for time-
dependent systems, E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984).
The extension to piece-wise analytic potentials and the initial-state dependence is addressed
in Memory in time-dependent density functional theory, N.T. Maitra, K. Burke, and C.
Woodward, Phys. Rev. Letts, 89, 023002 (2002).
For a simple demonstration of initial-state dependence, see Demonstration of initial-state
dependence in time-dependent density functional theory, N.T. Maitra and K. Burke, Phys.
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There was some controversy over the last step of the Runge-Gross proof, requiring the inte-
gration by parts, but this is settled in E.K.U. Gross and W. Kohn, in Advances in Quantum
Chemistry, Vol. 21: Density Functional Theory of Many-Fermion Systems, edited by S.
B. Trickey (Academic Press, San Diego, 1990).
