Remarks on time-dependent theory

Dirac s development of TDHF theory invokes the Heisenberg equation of motion for the density operator as a basic postulate, 

Equivalently, time-dependent canonical Hartree-Fock equations are assumed to take the same form as the time-dependent Schrodinger equation. 

These concepts, inherent in the TDHF formalism, generalize immediately to orbital functional theory, when electronic correlation energy is included in the model. Given some definition that determines a reference state for any 

Any postulated orbital functional E p, ] defines an action integral, 

Here G = Tt + vc, where H is defined by SEo/niSp = Tipi as in Hartree-Fock theory. vc is defined by the functional derivative = vcpi. If Ec is omitted, the theory reduces to TDHF. 

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