where Ai and A0 are two constants related through the normalization condition on the total wavefunction. A relation between the variational parameters a and ( can be obtained through the continuity condition at % = so that the energy functional is to be minimized with respect to only one parameter, either a or ( .

The energy of the ground state of H, H+, and HeH2+ for V0 = 0, 2, 8, 20 and mR^y is displayed in Figure 43 as a function of the size of the enclosing box %0. As can be noted, good agreement is found with the exact results for the case of V0 = m. When V0 has a finite value, the calculations show the correct qualitative behavior, similar to that found by Ley-Koo and Rubinstein [124] for hydrogen within penetrable spherical boxes. In order to gain some confidence in the value of the ansatz wavefunctions, we have calculated the polarizability and pressure for H+. In the Kirkwood approximation [119] the parallel and perpendicular components of the polarizability are given by

Finally, the pressure on the system due to the confinement can be calculated through the relationship

ds dV

where V is the volume of the spheroidal box and s is the total ground state energy of the system calculated at the equilibrium bond length. The results obtained for these properties are displayed in Figure 44 for V0 = 0 and mR^y as a function of %0. As can be seen, good agreement is found when our results are compared for V0 = m with the calculations reported by LeSar and Herschbach [109, 110], who used a five-term James-Coolidge variational wavefunction. For finite values of V0 the correct qualitative behavior is obtained [125].

3.9. Confinement of One- and Two-Electron Atomic Systems by Spherical Penetrable Boxes

We explicitly treat the case of some one- and two-electron atomic systems (H, H-, He, Li2+, and Be2+) in their ground state within spherical confining barriers [66]. 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

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