Determination of a Wave Function Functional
英文摘要：
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 $ψ$ to be a functional of a set of functions $χ: ψ= ψ[χ]$, 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 $χ$ such that the wave function functional $ψ[χ]$ 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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