Lecture VII : The Hohenberg-Kohn theorem and the Kohn-Sham equations
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چکیده
Proof I : Assume that there exist two potentials V (1) ext (~r) and V (2) ext (~r) differing by more than a constant and giving rise to the same ground state density, n(~r). Obviously, V (1) ext (~r) and V (2) ext (~r) belong to distinct Hamiltonians Ĥ (1) ext(~r) and Ĥ (2) ext(~r), which give rise to distinct wavefunctions Ψ (1) ext(~r) and Ψ (2) ext(~r). Because of the variational principle, no wavefunction can give an energy that is less than the energy of Ψ (1) ext(~r) for Ĥ (1) ext(~r). That is
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