Can anyone help me, I am some what unclear on the reason why "conventional" superconductors have cooper pairs only in the singlet state. Is it something to do with the expectation values given for the separate states calculated from their spacial and spin wave functions? For example does the singlet state with an even spacial wave function and an odd spin wave function give a lower Energy eigenvalue when operated on using the Hamiltonian compared to the triplet (spin anti parallel) state? Does BCS theory only predict singlet cooper pairs or just state that it is the more favorable ? I know that cooper pairs have a zero center of mass momentum and anti parallel spins. Is the the anti parallel spin due to the Pauli principle (would that matter as the cooper pair is essentially a composite boson?) or due to a lower expectation value given by the Hamiltonian?