COOPER PAIRING WITH A ONE-DIMENSIONAL DELTA-POTENTIAL

Measurements of quantized magnetic flux establish that pairing is empi rically present in all known superconductors, whether the old low-temp erature elemental ones or the newer high-temperature cuprates. The pai ring phenomenon is explained and derived, analytically and graphically , in a simple one-dimensional model with an attractive 6-potential. Th e model displays a smooth continuous evolution from the loosely-bound, strongly-overlapping Cooper pair extreme reminiscent of low-temperatu re, to the well-separated, tightly-bound composite bosons extreme more characteristic of high-temperature superconductivity. This latter pro perty makes it useful in addressing exotic superconductivity where str ong suggestions of a link with Bose condensation emerge from recent ex periments. The interaction model does not exhibit all the physical pro perties of actual electron-electron (or hole-hole) pairing forces in s uperconductors. However, it lends itself to a simple, pedagogically us eful solution at the Cooper problem level in terms of combined analyti cal, graphical and numerical techniques which are standard.