Solução da equação de Schrödinger unidimensional independente do tempo por redes neurais

Abstract

In this work, we present the time-independent solution for the one-dimensional Schrödinger equation, both through computational numerical methods and through the use of machine learning algorithms, in which the technique used was the resolution by neural networks. Throughout the procedure, the hyper-parameter test took place to build a more efficient neural network, in which it was used to solve this equation given a new potential, since its training set were potentials generated randomly along with their respective wavefunctions. In addition, there was a comparison between the numerical solution and the solution by neural networks for the known potentials of quantum mechanics, the infinite square well and the simple harmonic oscillator.