A pressure dependent Schrodinger equation is used to find the conditions that lead to superconductivity. When no pressure is exerted, the superconductor resistance vanishes beyond a critical temperature related to the repulsive force potential of the electron gass, where one assuming the electron total energy to be thermal, where applying mechanical pressure destroys Sc when it exceeds a certain critical value. However when the electron total energy is an assumed to be that of the free electron model and that the pressure is thermal and mechanical, the situation is different. The quantum expression for resistance shows that the increase of mechanical pressure increases the critical temperature. Such phenomenon is observed in high temperature cupper group.
Using plasma equations beside Maxwell statistical distribution law a useful expression of the Neel temperature similar to that obtained for high temperature superconductors was derived. This expression was found by obtaining a new expression of energy from the plasma equation. The same procedures were used to find an expression of the pressure and isotope mass in terms of the critical temperature for high temperature superconductors. These expressions resembles the conventional ones.
The Wave function of Schrodinger Equation is expressed in terms of time dependent energy eigen function and spatial dependent wave function in the energy space, which gives spatial energy probability. This equation is utilized to find quantum momentum dependent on temperature. This in turn is used to find quantum complex resistance. This expression shows that the superconducting resistance vanishes for temperatures less than a certain critical value. This result conforms to superconductor conventional theory and empirical relations. The application of external magnetic field destroys superconductivity when its strength exceeds a certain critical value. The expression of the relationship between the critical magnetic field and the critical temperature is typical to the conventional one. This is the first time to obtain the conventional relationship for the superconductor's resistance and critical magnetic field in one model in the energy space.
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