Use of the direct variational method for the study of one- and two-electron atomic systems confined by spherical penetrable boxes

An extension of the direct variational method to study quantum systems confined by penetrable potentials is proposed. The authors treat explicitly the case of some one- and two-electron atomic systems (H, H-, He, Li+ and Be2+) in their ground state within spherical confining barriers. In all cases, a simple representation for the ansatz wavefunction is employed and the corresponding energies are given as a function of size and height of the barrier. Additionally, some quantities of physical interest are evaluated for the case of hydrogen and comparison is made with available exact calculations.