Quantum Mechanism of Condensation and High Tc Superconductivity*

First, we introduce a new interpretation of quantum mechanical wave functions, by postulating that the wave function $\psi=|\psi| e^{i \varphi}$ is the common wave function for all particles in the same class determined by the external potential $V(x)$, $|\psi(x)|^2$ represents the distribution density of the particles, and $\frac{\hbar}{m} \nabla \varphi$ is the velocity field of the particles. Second, we show that for superconductivity, the formation of superconductivity comes down to conditions for the formation of electron-pairs, and for the electron-pairs to share a common wave function. Thanks to the recently developed PID interaction potential of electrons and the average-energy level formula of temperature, these conditions for superconductivity are explicitly derived. Furthermore, we obtain both microscopic and macroscopic formulas for the critical temperature. Third, we derive the field and topological phase transition equations for condensates, and make connections to the quantum phase transition, as a topological phase transition.