All explanations of Josephson effect I have read so far are based on Ginzburg–Landau theory. There seems no explanation based on Schrodinger equation. Why? While an explanation of Josephson frequency of 2eV/h seems not difficult to envisage, the major problem, I guess, should be with electron pairing. Josephson effect takes place with a driving voltage of less than 1mV, but a typical superconducting energy gap should be of 10meV or greater (especially for HTS), which should prevent electrons below the gap from being excited by phonons. Thus, how would an electron be driven to transit by a voltage of less than 1mV while it is prevented from transition by phonons of over 10meV? Do I miss or mistaken anything?