Advertisement

Pramana

, 89:70 | Cite as

Solving the two-dimensional Schrödinger equation using basis truncation: A hands-on review and a controversial case

Article

Abstract

Solutions of the Schrödinger equation by spanning the wave function in a complete basis is a common practice in many-body interacting systems. We shall study the case of a two-dimensional quantum system composed of two interacting spinless electrons and see that the correctness of the matrix approach depends inexplicably on the type of interaction existing between particles. Also, we shall extend the present study to other systems of special interest in order to ilustrate the method.

Keyword

Matrix mechanics quantum rings coupled harmonic oscillators 

PACS Nos

02.30.Mv 02.60.Dc 03.65.−w 03.65.Ge 

Notes

Acknowledgements

J Batle acknowledges fruitful discussions with J Rosselló, Maria del Mar Batle and Regina Batle. J Batle also appreciates fruitful discussions with Pierre-Francois Loos. All authors appreciate the advice given by the anonymous referees.

References

  1. 1.
    U Kaldor (Ed.), Many-body methods in quantum chemistry, Lecture notes in chemistry (Springer, Berlin, 1989)Google Scholar
  2. 2.
    E Dagotto, Rev. Mod. Phys. 667, 63 (1994)Google Scholar
  3. 3.
    Pierre-Francois Loos and Peter M W Gill, Phys. Lett. A 378, 329 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    Pierre-Francois Loos, Phys. Rev. A 81, 032510 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    S Flügge, Practical quantum mechanics (Springer, Berlin, 1999)MATHGoogle Scholar
  6. 6.
    Alireza Beygi, S P Klevansky and Carl M Bender, Phys. Rev. A 91, 062101 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  1. 1.Department of Physics, College of ScienceTaibah UniversityYanbuSaudi Arabia
  2. 2.Departament de FísicaUniversitat de les Illes BalearsPalma de MallorcaSpain
  3. 3.Department of Physics, Faculty of ScienceKing Abdulaziz University JeddahJeddahSaudi Arabia

Personalised recommendations