Contribution of Discrete and Continuum Wave Functions in the Ground State Polarizability of Hydrogen

We analytically derive a discrete radial Green function for a hydrogenic system in terms of associated Leguerre polynomials. We investigate the polarizability of the ground-state hydrogen using the so-called length gauge approximation of electrodynamics. The polarizability is the sum of the polarization matrix elements for the negative and the positive frequency values. We estimate the contribution of discrete wavefunctions to the static ground state polarizability. We found that the contribution of continuum states dominates over that of discrete states to the polarizability by an order of magnitude.