BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson-Gaudin exact wave function

► We develop a perturbation expansion for the Bardeen-Cooper-Schrieffer Hamiltonian. ► We show that deviations from mean-field results are underextensive for relevant operators for any order of the perturbation theory. ► We discuss the relation between the BCS wave function and the exact wave function, which can be found by using Richardson approach.