On a Repulsive Short-Range Potential Influence on the Harmonic Oscillator

We study the influence of a symmetrically spherical potential on the harmonic oscillator. The symmetrically spherical potential consists of a repulsive short-range potential inspired by the power-exponential potential. By dealing with s-wave in the region where the repulsive short-range potential is significant, we show how the energy levels of the three-dimensional harmonic oscillator are modified by the short-range potential influence. Furthermore, we show that a non-null revival time with regard to the s-state exists.