In this thesis, we investigate the Schrödinger-Lohe (S-L) model as a phenomenological model for quantum synchronization. In order to model real-world phenomena, we employ several dynamical structures such as a general network structure, interaction frustration and cubic nonlinearity and study their emergent behaviors. First, we begin with all-to-all network structure and show that the complete synchronization occurs for generic initial data. Next, we consider general network structure to observe several dynamic patterns including repulsive behavior and periodic orbits. Furthermore, we take account of interaction frustration which describes phase-lag effects and present sufficient frameworks leading to complete and practical synchronizations. Finally, we consider the cubic nonlinearity and harmonic potential to observe both periodic and synchronous behaviors.