IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3005-d686205.html
   My bibliography  Save this article

Accidental Degeneracy of an Elliptic Differential Operator: A Clarification in Terms of Ladder Operators

Author

Listed:
  • Roberto De Marchis

    (MEMOTEF, Faculty of Economics, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
    These authors contributed equally to this work.)

  • Arsen Palestini

    (MEMOTEF, Faculty of Economics, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
    These authors contributed equally to this work.)

  • Stefano Patrì

    (MEMOTEF, Faculty of Economics, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
    These authors contributed equally to this work.)

Abstract

We consider the linear, second-order elliptic, Schrödinger-type differential operator L : = − 1 2 ∇ 2 + r 2 2 . Because of its rotational invariance, that is it does not change under S O ( 3 ) transformations, the eigenvalue problem − 1 2 ∇ 2 + r 2 2 f ( x , y , z ) = λ f ( x , y , z ) can be studied more conveniently in spherical polar coordinates. It is already known that the eigenfunctions of the problem depend on three parameters. The so-called accidental degeneracy of L occurs when the eigenvalues of the problem depend on one of such parameters only. We exploited ladder operators to reformulate accidental degeneracy, so as to provide a new way to describe degeneracy in elliptic PDE problems.

Suggested Citation

  • Roberto De Marchis & Arsen Palestini & Stefano Patrì, 2021. "Accidental Degeneracy of an Elliptic Differential Operator: A Clarification in Terms of Ladder Operators," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3005-:d:686205
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3005/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3005/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arsen Palestini, 2022. "Preface to the Special Issue “Mathematical Modeling with Differential Equations in Physics, Chemistry, Biology, and Economics”," Mathematics, MDPI, vol. 10(10), pages 1-2, May.

    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:9:y:2021:i:23:p:3005-:d:686205. 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.