Energy-Embedded Neural Solvers for One-Dimensional Quantum Systems

TL;DR

This paper introduces an energy-embedding physics-informed neural network that accurately solves one-dimensional quantum Schrödinger equations, including various potentials, demonstrating high accuracy and adaptability for quantum physics applications.

Contribution

The paper presents a novel energy-embedding neural network approach for solving Schrödinger equations, improving accuracy and extending applicability to different potentials and higher-dimensional systems.

Findings

High accuracy in solving various quantum potentials

Effective in calculating ground and excited states

Demonstrates adaptability to different PDEs

Abstract

Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving the one-dimensional time-independent Schr\"{o}dinger equation to obtain ground- and excited-state wave functions, as well as energy eigenvalues by incorporating an embedding layer to generate process-driven data. The method demonstrates high accuracy for several well-known potentials, such as the infinite potential well, harmonic oscillator potential, Woods-Saxon potential, and double-well potential. Further validation shows that the method also performs well in solving the radial Coulomb potential equation, showcasing its adaptability and extensibility. The proposed approach can be extended to solve other partial differential equations beyond the Schr\"{o}dinger equation and holds promise for applications in high-dimensional quantum systems.