• Bound States of Spherically Symmetric Potentials: Heat Capacity Calculations

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/025/11/1491-1506

    • Keywords

       

      Schrodinger equation, degeneracy, quantum models.

    • Abstract

       

      We solve the time-independent Schro¨dinger equation for spher-ically symmetric potentials. First, we consider simple cases of a particle on a ring and a particle on a sphere to illustrate the degeneracy arising due to symmetry. We then consider three different spherically symmetric potentials: (i) spherical well potential, (ii) isotropic three-dimensional harmonic oscillator, and (iii) spherically confined isotropic three-dimensional har-monic oscillator. Our discussion mainly focuses on the energy levels of the bound states and the associated degeneracies. Finally, we calculate the heat capacity of endohedral fullerenes using two simple models—particle in a spherical box and con-fined harmonic oscillator.

    • Author Affiliations

       

      Chandan Kumar1

      1. Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City SAS Nagar, Sector 81, Mohali 140 306, Punjab.
    • Dates

       
  • Resonance – Journal of Science Education | News

© 2021-2022 Indian Academy of Sciences, Bengaluru.