The BCS theory amended

In the standard theory of superconductivity a quasiparticle excitation changes the energy of the system by the quasiparticle energy. But the number of excitations determine also the gap energy which further determines the energy of the condensate and the energy spectrum of quasiparticles. Such extra contributions to the total energy of the system--which are not taken into account in the standard formalism--led us to a redefinition of the quasiparticle energies and of the quasiparticle populations by the usual method of the maximization of the superconductor partition function. The result of this correction is a critical temperature which is lower than the BCS critical temperature and a finite jump of the energy gap at the phase transition. The discontinuity of the energy gap at the critical temperature marks a first order phase transition which is also in disagreement with the standard BCS interpretation. The fact that the standard BCS formalism is theoretically inconsistent is revealed in the calculation of the heat capacity and of the internal energy. These inconsistencies are removed in our formulation. The purpose of our paper is not to adjust the theory to better describe the phenomenology of superconductivity, but to reevaluate and amend the BCS formalism.