Spectral characterization of hydrogen-like atoms confined by oscillating systems

The spectral characterization of Coulomb systems confined by a homogeneous pseudo-Gaussian oscillator is investigated. This is done using the efficient computational method of generating functionals. Also, this method is used for the spectral characterization of homogeneous harmonic oscillator confinement, treated as a particular case of pseudo-Gaussian oscillator confinement. Finally, confinement by an impenetrable sphere of finite radius is considered by studying its conjugate effect along with a harmonic oscillator.