The confined hydrogen atom: a linear variational approach

We study the size effect on the confinement of a hydrogen atom in a spherical box of impenetrable walls. We compute the energy of the ground and a few excited states as a function of the box radius R-c. To obtain the energy eigenvalues and eigenfunctions we utilize the linear variational method via a basis set of free-particle-in-a-box wave functions. For small values of R-c convergence is attained with a small number of basis set functions, whereas for R-c >= 5.0 au, it is necessary to use over 100 terms in the expansion.