Using the Bethe-Salpeter (BS) equation, Cooper pairing can be generalized to
include contributions from holes as well as particles from the ground state of
either an ideal Fermi gas (IFG) or of a BCS many-fermion state. The BCS model
interfermion interaction is employed throughout. In contrast to the
better-known original Cooper pair problem for either two particles or two
holes, the generalized Cooper equation in the IFG case has no real-energy
solutions. Rather, it possesses two complex-conjugate solutions with purely
imaginary energies. This implies that the IFG ground state is unstable when an
attractive interaction is switched on. However, solving the BS equation for the
BCS ground state reveals two types of {\it real} solutions: one describing
moving (i.e., having nonzero total, or center-of-mass, momenta) Cooper pairs as
resonances (or bound composite particles with a {\it finite} lifetime), and
another exhibiting superconducting collective excitations sometimes known as
Anderson-Bogoliubov-Higgs (ABH) modes. A Bose-Einstein-condensation-based
picture of superconductivity is addressed.Comment: 5 pages in PS, including 3 figures. In press Physica