Electronic structure of superconductors with dilute magnetic impurities

The Bogoliubov equations for the quasiparticle eigenfunctions of a superconductor with isolated magnetic impurities are derived. Impurity scattering is treated in the Born approximation, and the wave functions in the spatially varying pair potential are calculated by the WKBJ method of Bardeen, K\"ummel, Jacobs, and Tewordt. The pair-breaking condition is established, and the spatial variation of the pair potential at the impurity site is determined for temperatures near the critical temperature and the absolute zero. A few bound states are found in the pair-potential well. The free energy is obtained as a function of a variational parameter and shows an increase due to the energies of the pair-broken states.