We report theoretical studies on the newly discovered novel Josephson effect and scanning tunneling spectroscopy (STS) at the interface of strontium titanate/lanthanum aluminate (STO/LAO).With a phenomenological boson-fermion model,the density of states is calculated and the results are consistent with the STS experiments.A typical calculation of Josephson effect is performed,and it is in qualitative agreement with the experiments.The calculations indicate that the gap states come from the pairing of quasi-particles with a finite total momentum and the Josephson current comes from the tunneling of quasi-particle pairs with zero momentum.The quasi-particles are Bogoliubov quasi-particles.Moreover,the fits using Kulik’s formula imply that the Josephson junction at the STO/LAO interface has a point contact with the clean superconductor limit.