A study of the confined 2D isotropic harmonic oscillator in terms of the annihilation and creation operators and the infinitesimal operators of the SU(2) group

Abstract

The eigenspectral properties of the 2D isotropic harmonic oscillator, centrally enclosed in the symmetric box with impenetrable walls, are studied for the first time using the annihilation and creation operators and the infinitesimal operators of the SU(2) group. It is shown explicitly how the imposition of the Dirichlet boundary condition at a certain uniquely prescribed confinement radius leads to the energy difference of two harmonic oscillator units between all successive pairs of the confined states, defined by the projection angular momentum quantum numbers [m, m±2] such that the lowest energy state corresponding to the chosen m is excluded in the first pair.