The Hydrogen and Helium Atoms Confined in Spherical Boxes

The most relevant, and often utilized, methods and techniques for obtaining energy levels of confined one- and two-electron atoms are reviewed. We discuss how the electronic states of hydrogen and helium atoms are remarkably modified when subjected to extreme pressure regimes. For the hydrogen atom confined in a spherical box of impenetrable walls, we present the exact solutions and the energy eigenvalues obtained with very high accuracy. A few wave function properties calculated for the confined hydrogen atom, such as pressure, polarizability and the Fermi contact term, are discussed in some detail. Some accurate energy calculations for the hydrogen atom confined in a penetrable spherical box and when subjected to Neumann boundary conditions, are also presented. In addition, for the spherically confined helium atom we present the most accurate calculations reported to date. © 2009 Elsevier Ltd. All rights reserved.