Energy, polarizability and size of confined one-electron systems

The energy, ground-state properties, polarizability and dipole shielding factor of one-electron systems confined in boxes are studied as functions of box size, R. The systems are the unbound electron, hydrogenic atom, harmonic oscillator and z 2p oscillators in various 1D and 3D boxes (cartesian and spherical). Exact polarizabilities α are compared with the variational Kirkwood, Buckingham and Unsöld bounds. For all boxes with an attractive internal potential the curve α(R) has a characteristic s shape. Some discussion of α(R) for ions in crystals in given in terms of these models.