  Cooper's original one pair problem in continuum is revisited here
corresponding to a lattice of tight binding nature, with an aim to investigate
superconductivity in low dimensional systems. An electronic type of boson
mediated attraction is considered for the pairing mechanism with the non
trivial energy dependence of the electronic density of states taken into
account in the calculation in a rigorous way. Some of the very important
electronic and optical properties of a class of one dimensional organic
conductors are used for the development of the formalism and calculation. The
result of our calculations show that fermionic pair formation is indeed
possible with some constraints. Similarities emerge in the physical properties
of the electron pair formed from Cooper's treatment and ours excepting the
striking difference appearing in the form of occurrence of a maximum allowed
band filling for pairing and of an upper bound of the pairing energy found in
our approach.
