Self-Consistent Pair Potential in an Inhomogeneous Superconductor

De Gennes's equations for the Bogoliubov amplitudes in an inhomogeneous superconductor are solved in a simple geometry with the use of a one-parameter Ansatz for the pair potential. The solutions are used to determine the parameter self-consistently. In the limit $T\to T_c$, the results agree with the Ginzburg-Landau theory, but the present method is applicable at all temperatures $T<\mathrm{}{T}_c$.