both in the interior as well as in the exterior region. Note that the preceding arguments are of a general character and should apply to any system whether confined by penetrable or impenetrable walls.

3.9.2. Ground State of the Confined Hydrogen Atom

The potential energy associated with the Hamiltonian of the hydrogen atom confined by a spherical box with penetrable walls is given by a Coulomb term inside the box

r < rn and a constant barrier height outside the box,

with r0 the radius of the confining box.

For the purposes of this section we consider now the 1s state. For this case, the corresponding wavefunctions are chosen as

Xiils) = Niiro - yr)expi-ar) r <ro Xoils) = Nor-l expi-ßr) r > rQ

with a, 3, and y variational parameters and Nt and No normalization constants.

In contrast to the impenetrable case, we have considered three variational parameters in order to allow for more flexibility in the matching procedure at the boundary. In fact, only two of these parameters (a, y) need to be found, the third one being defined through Eq. (235) as

Following Ley-Koo and Rubinstein [124], some quantities of physical interest such as the Fermi contact term (A), diamagnetic screening constant (a), polarizability (a), and pressure (P) are defined, respectively, as

3ac2\ r

0 0

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