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