Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure

Carlos R. Handy, Daniel Vrinceanu, Carl B. Marth and Harold A. Brooks
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Carlos R. Handy: Department of Physics, Texas Southern University, Houston, TX 77004, USA
Daniel Vrinceanu: Department of Physics, Texas Southern University, Houston, TX 77004, USA
Carl B. Marth: Dulles High School, Sugar Land, TX 77459, USA
Harold A. Brooks: Department of Physics, Texas Southern University, Houston, TX 77004, USA

Mathematics, 2015, vol. 3, issue 4, 1-24

Abstract: Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrödinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states (generated through the power moments) can define an L2 convergent, non-orthonormal, basis expansion with sufficient pointwise 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 The quantization approach pursued here defines an alternative strategy emphasizing the relevance of OPPQ to the reconstruction of the local structure of the physical states.

Keywords: weighted polynomial expansions; moment representations; Hill determinant method; algebraic quantization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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