Pointwise reconstruction of wave functions from their moments through weighted polynomial expansions: an alternative global-local quantization procedure

Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrodinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states (generated through the power moments) can define both an $L^2$ convergent, non-orthogonal, basis expansion with sufficient point-wise convergent behaviors enabling the direct coupling of the global (power moments) and local (Taylor series) expansions in configuration space. Our formulation is elaborated within the orthogonal polynomial projection quantization (OPPQ) configuration space representation previously developed by Handy and Vrinceanu. The quantization approach pursued here defines an alternative strategy emphasizing the relevance OPPQ to the reconstruction of the local structure of the physical states.