Superconductivity is one of the most important phenomena in solid state physics. Its theoretical framework at low critical temperature T_c is based on Bardeen, Cooper and Schrieffer theory (BCS). But at high T_c above 135, this theory suffers from some setbacks. It cannot explain how the resistivity abruptly drops to zero below T_c , besides the explanation of the so called pseudo gap, isotope and pressure effect, in addition to the phase transition from insulating to super-conductivity state. The models proposed to cure this drawback are mainly based on Hubbard model which has a mathematical complex framework. In this work a model based on quantum mechanics besides generalized special relativity and plasma physics. It is utilized to get new modified Schr?dinger equation sensitive to temperature. An expression for quantum resistance is also obtained which shows existence of critical temperature beyond which the resistance drops to zero. It gives an expression which shows the relation between the energy gap and T_c . These expressions are mathematically simple and are in conformity with experimental results.