Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

Abstract

This article presents an approach to the two-dimensional Schrödinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential, starting from the knowledge of the solutions to a large number of arbitrary sample problems. A network architecture with two hidden layers is proposed to predict the wave function and energy of the ground state. Several accuracy indicators are proposed for validating the estimates provided by the neural network. The testing of the trained network is done by applying it to a large set of confinement potentials different from those used in the learning process. Some particular cases with symmetrical potentials are solved as concrete examples, and a good network prediction accuracy is found.

arXiv comment29 pages, 13 figures, 2 tables

References in corpus (15)

• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• Asymptotic iteration method for eigenvalue problems
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Droplet Epitaxy of Semiconductor Nanostructures for Quantum Photonic Devices
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Deep learning and the Schrödinger equation
• Artificial Neural Network Methods in Quantum Mechanics
• Double wells, scalar fields and quantum phase transitions in ions traps
• Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase
• Electro-optical properties of phosphorene quantum dots
• Nuclear binding energy predictions using neural networks: Application of the multilayer perceptron
• Variational Sturmian Approximation: A nonperturbative method of solving time-independent Schrödinger equation
• Energy Levels of One Dimensional Anharmonic Oscillator via Neural Networks
• Asymptotic Iteration and Variational Methods for Gaussian Potential