dorsal/arxiv
View SchemaDetermination of a Wave Function Functional
| Authors | Xiao-Yin Pan, Viraht Sahni, Lou Massa |
|---|---|
| Categories | |
| ArXiv ID | physics/0402066 |
| URL | https://arxiv.org/abs/physics/0402066 |
| DOI | 10.1103/PhysRevLett.93.130401 |
Abstract
In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather than a function. In this manner a greater flexibility to the structure of the wave function is achieved. A constrained search in a subspace over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a constraint such as normalization or the Fermi-Coulomb hole charge sum rule, or the requirement that it lead to a physical observable such as the density, diamagnetic susceptibility, etc. is then performed. A rigorous upper bound to the energy is subsequently obtained by variational minimization with respect to the parameters in the approximate wave function functional. Hence, the terminology, the constrained-search variational method. The \emph{rigorous} construction of such a constrained-search--variational wave function functional is demonstrated by example of the ground state of the Helium atom.
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"abstract": "In this paper we propose the idea of expanding the space of variations in\nstandard variational calculations for the energy by considering the wave\nfunction $\\psi$ to be a functional of a set of functions $\\chi: \\psi =\n\\psi[\\chi]$, rather than a function. In this manner a greater flexibility to\nthe structure of the wave function is achieved. A constrained search in a\nsubspace over all functions $\\chi$ such that the wave function functional\n$\\psi[\\chi]$ satisfies a constraint such as normalization or the Fermi-Coulomb\nhole charge sum rule, or the requirement that it lead to a physical observable\nsuch as the density, diamagnetic susceptibility, etc. is then performed. A\nrigorous upper bound to the energy is subsequently obtained by variational\nminimization with respect to the parameters in the approximate wave function\nfunctional. Hence, the terminology, the constrained-search variational method.\nThe \\emph{rigorous} construction of such a constrained-search--variational wave\nfunction functional is demonstrated by example of the ground state of the\nHelium atom.",
"arxiv_id": "physics/0402066",
"authors": [
"Xiao-Yin Pan",
"Viraht Sahni",
"Lou Massa"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevLett.93.130401",
"title": "Determination of a Wave Function Functional",
"url": "https://arxiv.org/abs/physics/0402066"
},
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