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

  • Molecular Physics and Chemical Physics
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Abstract.

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.

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Authors and Affiliations

  1. Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700 032, India

    N. Bera & J. K. Bhattacharjee

  2. Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur, 721 302, India

    S. Mitra & S. P. Khastgir

Authors
  1. N. Bera
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  2. J. K. Bhattacharjee
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  3. S. Mitra
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  4. S. P. Khastgir
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Correspondence to J. K. Bhattacharjee.

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Bera, N., Bhattacharjee, J., Mitra, S. et al. Energy levels of a particle confined in a super-circular box. Eur. Phys. J. D 46, 41–50 (2008). https://doi.org/10.1140/epjd/e2007-00282-6

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  • DOI: https://doi.org/10.1140/epjd/e2007-00282-6

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