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Articles 91 - 94 of 94
Full-Text Articles in Physical Sciences and Mathematics
Hohenberg-Kohn Theorem Including Electron Spin, Xiao-Yin Pan, Viraht Sahni
Hohenberg-Kohn Theorem Including Electron Spin, Xiao-Yin Pan, Viraht Sahni
Publications and Research
The Hohenberg-Kohn theorem is generalized to the case of a finite system of N electrons in external electrostatic epsilon(r) = -del nu(r) and magnetostatic B(r) = del x A(r) fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density rho(r) and physical current density j(r) and the potentials {nu(r), A(r)}. The possible many-to-one relationship between the potentials {v(r), A(r)} and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables …
Hohenberg-Kohn And Percus-Levy-Lieb Proofs Of Density-Functional Theory, Viraht Sahni, Xiao-Yin Pan
Hohenberg-Kohn And Percus-Levy-Lieb Proofs Of Density-Functional Theory, Viraht Sahni, Xiao-Yin Pan
Publications and Research
The premise of density-functional theory is that knowledge of the ground-state density uniquely determines the Hamiltonian, and thereby, via solution of the corresponding time-independent Schrodinger equation, all the properties of the system. The density therefore constitutes a basic variable of quantum mechanics. There are at present two paths from the density to the Hamiltonian: the Hohenberg and Kohn proof of the bijectivity between the external potential and the basic variable, and the Percus, Levy, and Lieb constrained-search proof. We argue the Hohenberg- and Kohn-type proof to be the more fundamental, and that this is the case in general when both …
Demonstration Of The Gunnarsson-Lundqvist Theorem And The Multiplicity Of Potentials For Excited States, Yu-Qi Li, Xiao-Yin Pan, Biao Li, Viraht Sahni
Demonstration Of The Gunnarsson-Lundqvist Theorem And The Multiplicity Of Potentials For Excited States, Yu-Qi Li, Xiao-Yin Pan, Biao Li, Viraht Sahni
Publications and Research
The Gunnarsson-Lundqvist (GL) theorem of density functional theory states that there is a one-to-one relationship between the density of the lowest nondegenerate excited state of a given symmetry and the external potential. As a consequence, knowledge of this excited state density determines the external potential uniquely. [The GL theorem is the equivalent for such excited states of theHohenberg-Kohn (HK) theorem for nondegenerate ground states.] For other excited states, there is no equivalent of the GL or HK theorem. For these states, there thus exist multiple potentials that generate the excited-state density. We show, by example, the satisfaction that the GL …
Wave-Function Functionals For The Density, Marlina Slamet, Xiao-Yin Pan, Viraht Sahni
Wave-Function Functionals For The Density, Marlina Slamet, Xiao-Yin Pan, Viraht Sahni
Publications and Research
We extend the idea of the constrained-search variational method for the construction of wave-function functionals psi[chi] of functions chi. The search is constrained to those functions chi such that psi[chi] reproduces the density rho(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals psi[chi] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals psi[chi] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle …