Justification for the group-theoretical method as the right way to solve the infinite spherical well in quantum mechanics

Abstract

Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to further justifying the group-theoretical method, the problem is first studied from the viewpoint of classical mechanics. Then the radial probability densities predicted by classical mechanics are compared with those predicted from solutions of the problem obtained by the group-theoretical method. The comparisons clearly indicate the convergence of predictions of quantum mechanics and classical mechanics in the limit of large eigen-energies. Therefore, the group-theoretical method is justified as the right way to solve the problem of the infinite spherical well.