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

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