Deep learning equation-driven approaches, also known as physics-informed neural networks (PINNs), have seen a wave of success in modeling physical systems governed by differential equations. However, these techniques have rarely been applied to quantum systems, where traditional numerical methods provide accurate solutions but become computationally expensive for large-scale systems. We explore a neural network approach capable of solving the Schrödinger equation for two-dimensional systems of periodic potentials.Applying efficient sampling and normalization constraints allows the simultaneous discovery of the energy band structure and the associated wavefunctions, that are crucial, for example, to determine the properties of electronic, photonic, and metamaterials systems.