2005/06/23 by Xiao‐Yin Pan, Xiao-Yin Pan, Viraht Sahni +1
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Combinatorics #Energy (signal processing) #Excited state #Ground state #Hermitian matrix #Mathematical physics #Mathematics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Wave function #physics.atom-ph #physics.chem-ph
paper · pdf · doi:10.1103/physreva.72.032505
26 pages, 4 figures, 5 tables
arxiv created 2005/06/23 · openalex publication_date 2005/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a recent paper [Phys. Rev. Lett. 93, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function \ensuremathψ to be a functional of functions \ensuremathχ, \ensuremathψ=\ensuremathψ[\ensuremathχ], rather than a function. A constrained search is first performed over all functions \ensuremathχ such that the wave-function functional \ensuremathψ[\ensuremathχ] satisfies a physical constraint or leads to the known value of an observable. A rigorous upper bound to the energy is then obtained via the variational principle. In this paper we generalize the constrained-search variational method, applicable to both ground and excited states, to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. We construct analytical three-parameter ground-state functionals for the H^\ensuremath- ion and the He atom through the constraint of normalization. We present the results for the total energy E, the expectations of the single-particle operators W=\ensuremath∑irin, n=\ensuremath-2,\ensuremath-1,1,2, W=\ensuremath∑i\ensuremathδ(ri), and W=\ensuremath∑i\ensuremathδ(ri\ensuremath-r), the structure of the nonlocal Coulomb hole charge \ensuremathρc(rr^\ensuremath'), and the expectations of the two particle operators u2,u,1∕u,1∕u2, where u=\ensuremath|ri\ensuremath-rj\ensuremath|. The results for all the expectation values are remarkably accurate when compared with the 1078-parameter wave function of Pekeris, and other wave functions that are not functionals. We conclude by describing our current work on how the constrained-search variational method in conjunction with quantal density-functional theory is being applied to the many-electron case.