Bound States of Spherically Symmetric Potentials: Heat Capacity Calculations
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.
Volume 26 | Issue 1