IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v3y2015i4p1045-1068d58370.html
   My bibliography  Save this article

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

Author

Listed:
  • Carlos R. Handy

    (Department of Physics, Texas Southern University, Houston, TX 77004, USA
    These authors contributed equally to this work.)

  • Daniel Vrinceanu

    (Department of Physics, Texas Southern University, Houston, TX 77004, USA
    These authors contributed equally to this work.)

  • Carl B. Marth

    (Dulles High School, Sugar Land, TX 77459, USA
    These authors contributed equally to this work.)

  • Harold A. Brooks

    (Department of Physics, Texas Southern University, Houston, TX 77004, USA
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Carlos R. Handy & Daniel Vrinceanu & Carl B. Marth & Harold A. Brooks, 2015. "Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure," Mathematics, MDPI, vol. 3(4), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:4:p:1045-1068:d:58370
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/3/4/1045/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/3/4/1045/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:3:y:2015:i:4:p:1045-1068:d:58370. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.