EFFECT OF PARTICLE-HOLE EXCITATIONS ON THE BCS GROUND STATE

Abstract

We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.