Schr\"odinger Equation

The Schrödinger equation is a fundamental equation in quantum mechanics describing the evolution of a quantum system's wave function. Current research focuses on developing efficient numerical methods for solving this equation, particularly for complex systems, employing machine learning techniques such as neural networks (including physics-informed neural networks and normalizing flows), restricted Boltzmann machines, and genetic algorithms to improve accuracy and computational speed. These advancements are significantly impacting fields like quantum chemistry and materials science by enabling more accurate simulations of molecular and material properties, and are also finding applications in areas such as machine learning theory and optimal transport.