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 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 conve...

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Bibliographic Details
Published in:Mathematics (Basel) 2015-12, Vol.3 (4), p.1045-1068
Main Authors: Handy, Carlos, Vrinceanu, Daniel, Marth, Carl, Brooks, Harold
Format: Article
Language:English
Subjects:
algebraic quantization
Hill determinant method
moment representations
weighted polynomial expansions
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math3041045