Hermite Neural Network Simulation for Solving the 2D Schrodinger
  Equation
Kourosh Parand Aida Pakniyat
The Schrodinger equation is a mathematical equation describing the wave
function's behavior in a quantum-mechanical system. It is a partial
differential equation that provides valuable insights into the fundamental
principles of quantum mechanics. In this paper, the aim was to solve the
Schrodinger equation with sufficient accuracy by using a mixture of neural
networks with the collocation method base Hermite functions. Initially, the
Hermite functions roots were employed as collocation points, enhancing the
efficiency of the solution. The Schrodinger equation is defined in an infinite
domain, the use of Hermite functions as activation functions resulted in
excellent precision. Finally, the proposed method was simulated using MATLAB's
Simulink tool. The results were then compared with those obtained using
Physics-informed neural networks and the presented method.