Determination of a Wave Function Functional

We propose expanding the space of variations in traditional 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. A constrained search in a subspace over all functions $\chi$ such that the functional $\psi [\chi ]$ satisfies a sum rule or leads to a physical observable is then performed. An upper bound to the energy is subsequently obtained by variational minimization. The rigorous construction of such a constrained-search–variational wave function functional is demonstrated.