We use the two dimensional extended Hubbard Hamiltonian with the position of the attractive potential as a variable parameter, within a BCS type approach, to study the interplay between the superconductor transition temperature Tc and hole content for high temperature superconductors. This method gives some insight on the range and intensity of the Cooper pair interaction. It suggests why different compounds have different values for their measured coherence lengths, and describes the experimental results of the superconducting phase diagram Tc × n . The calculations may also be used to study the effect of the applied pressure with the assumption that it increases the attractive potential which is accompanied by an increase in the superconductor gap. In this way we obtain a microscopic interpretation for the intrinsic term and a general expansion for Tc in terms of the pressure which reproduces well the experimental measurements on the Bi2Sr2CaCu2O8+y superconductors.
