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Mathematics 2015, 3(4), 1045-1068; doi:10.3390/math3041045

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

1
Department of Physics, Texas Southern University, Houston, TX 77004, USA
2
Dulles High School, Sugar Land, TX 77459, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Zhongqiang Zhang
Received: 15 July 2015 / Revised: 15 October 2015 / Accepted: 26 October 2015 / Published: 5 November 2015
View Full-Text   |   Download PDF [592 KB, uploaded 5 November 2015]   |  

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. View Full-Text
Keywords: weighted polynomial expansions; moment representations; Hill determinant method; algebraic quantization weighted polynomial expansions; moment representations; Hill determinant method; algebraic quantization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Handy, C.R.; Vrinceanu, D.; Marth, C.B.; Brooks, H.A. Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure. Mathematics 2015, 3, 1045-1068.

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