The superconductor theory based on the electron pair is reviewed and several viewpoints are proposed. A demonstrated case reveals the speed of each electron in the electron pair at Fermi level about 1.82x10^6 m/s in Pb. However, the fastest longitudinal and transverse speeds of crystal waves in Pb at 0 K are 2.18x10^3 m/s and 1.29x10^3 m/s in [100] direction, respectively. It seems to be very hard even impossible that the mediated phonon can real-time transfer momentum and energy between two so high-speed and antiparallel-momentum electrons in the superconducting state. In this research, we focus on single electron based on the experiments of Transmission Electron Microscopy. The new fitting temperature-dependent model for the London penetration depth is proposed. This model is much better than the one- and two-gap models and matches three experimental data much well. Then it further gives the temperature-dependent effective electron mass for the Nb superconductor film. Finally, the expression for the resistivity is deduced which can explain why the resistance is almost zero in the superconductor. All these new results are obtained by using the concept of single electron.