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    • Keywords


      Energy spectrum; degeneracies; statistical properties

    • Abstract


      In some simple quantum mechanical systems, the degeneracy of typical energy levels grows as a power of the energy or size. We ask whether, after dividing out this average growth, there is a well defined probability distribution of scaled degeneracies in the limit of large size or energy. The answer is yes, for a free particle in a sphere or cube. For the sphere, the distribution of scaled degeneracies is shown to follow a circular law. For the cube, a numerical study shows that the distribution rises linearly for low values of the scaled degeneracy and decays exponentially for large values.

    • Author Affiliations


      Mustansir Barma1 V Subrahmanyam1

      1. Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400 005, India
    • Dates

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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