The European Physical Journal D

, Volume 46, Issue 1, pp 41–50 | Cite as

Energy levels of a particle confined in a super-circular box

  • N. Bera
  • J. K. Bhattacharjee
  • S. Mitra
  • S. P. Khastgir
Molecular Physics and Chemical Physics


We find the energy levels of a free particle confined in a two dimensional infinite potential well having super-circular boundary (|x|n+|y|n=an where n is a rational number and a is a positive real number) by perturbing about the equivalent circle (n=2). The ground state energies are very accurate over a wide range of n and can be improved further by introducing a phenomenological constant determined from the knowledge of exact results available for diamond (n=1). For excited states, we find that the shape effect can cause parametric resonance which can lead to singlet-triplet crossing.


03.65.-W Quantum mechanics 31.15.Md Perturbation theory 03.65.Ge Solutions of wave equations: bound states 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • N. Bera
    • 1
  • J. K. Bhattacharjee
    • 1
  • S. Mitra
    • 2
  • S. P. Khastgir
    • 2
  1. 1.Department of Theoretical PhysicsKolkataIndia
  2. 2.Department of Physics and MeteorologyIndian Institute of TechnologyKharagpurIndia

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