Solving the Schrödinger equation in Higher Dimensions With Physics-Informed Neural Networks

Sammanfattning

Physics-Informed Neural Networks (PINNs) are a type of neural network that specializes in solving Partial Differential Equations (PDEs). In this thesis, we implement a PINN to solve the Schrödinger equation in higher spatial dimensions. The Schrödinger equation in higher spatial dimensions is extremely computationally intensive to solve and there have not been many articles focusing on this task. We aim to solve the isotropic harmonic oscillator, the anisotropic harmonic oscillator, and the Woods-Saxon potential. We also perform experiments to evaluate the model’s performance. The research aims to investigate what degree of precision the model can achieve on the potentials. For potentials with analytical solutions, this is answered by calculating the average relative error. The purpose of this study is to develop models and enable new ideas to solve the larger problem known as the many- body problem. The neural network is capable of finding the ground as well as excited states of multiple potentials. However, the effects of the curse of dimensionality persists.