IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v21y2010i11ns0129183110015919.html
   My bibliography  Save this article

Solving The Time-Dependent Schrödinger Equation With Absorbing Boundary Conditions And Source Terms In Mathematica 6.0

Author

Listed:
  • F. L. DUBEIBE

    (Facultad de Ciencias Humanas y de la Educación, Escuela de Pedagogía y Bellas Artes, Universidad de los Llanos, Villavicencio, Colombia)

Abstract

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schrödinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into these schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schrödinger equation by using a standard Crank–Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of theN × Nmatrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.

Suggested Citation

  • F. L. Dubeibe, 2010. "Solving The Time-Dependent Schrödinger Equation With Absorbing Boundary Conditions And Source Terms In Mathematica 6.0," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(11), pages 1391-1406.
    • Handle: RePEc:wsi:ijmpcx:v:21:y:2010:i:11:n:s0129183110015919
    DOI: 10.1142/S0129183110015919
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183110015919
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183110015919?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:wsi:ijmpcx:v:21:y:2010:i:11:n:s0129183110015919. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.