The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally "true" Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label "constant $〈H〉$ " for this form of time-dependent Hartree-Fock theory.NUCLEAR REACTIONS Unique time-dependent Hartree-Fock Hamiltonian obtained from variational principle by norm-violating variations.The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally "true" Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label "constant $〈H〉$" for this form of time-dependent Hartree-Fock theory.NUCLEAR REACTIONS Unique time-dependent Hartree-Fock Hamiltonian obtained from variational principle by norm-violating variations.

Physical Review CAug 1, 19797 citations

Time-Dependent Hartree-Fock and its Extension

正俊山村, 惇栗山

素粒子論研究Jul 20, 19840 citations

Time-dependent hartree-fock method and its extension

日本物理学会, 京都大学基礎物理学研究所, 正俊山村 +1 more

Jan 1, 19871 citation

Generalized variational principle for the time-dependent Hartree-Fock equations for a Slater determinant

Hans-Jörg Kull, Dieter Pfirsch

The time-dependent Hartree-Fock equations are derived from a variational principle for the general N-body action of a Slater determinant of single-electron orbitals. The variational principle generalizes commonly used variational treatments based on reduced two-body actions. The self-consistent field equations are found to contain time-dependent corrections to the standard mean-field interactions. Their physical significance is discussed and a time-dependent phase shift to the Slater determinant is obtained that properly accounts for the total interaction energy in the mean-field approach.The time-dependent Hartree-Fock equations are derived from a variational principle for the general N-body action of a Slater determinant of single-electron orbitals. The variational principle generalizes commonly used variational treatments based on reduced two-body actions. The self-consistent field equations are found to contain time-dependent corrections to the standard mean-field interactions. Their physical significance is discussed and a time-dependent phase shift to the Slater determinant is obtained that properly accounts for the total interaction energy in the mean-field approach.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMay 1, 200019 citations

〈H〉

" for this form of time-dependent Hartree-Fock theory.NUCLEAR REACTIONS Unique time-dependent Hartree-Fock Hamiltonian obtained from variational principle by norm-violating variations.