Physical Review A

Neural-network-based multistate solver for a static Schrödinger equation

Hong Li, Qilong Zhai, Jeff Z. Y. Chen

Published Mar 8, 2021• 31 citations

Abstract

Solving a multivariable static Schr\"odinger equation for a quantum system, to produce multiple excited-state energy eigenvalues and wave functions, is one of the basic tasks in mathematical and computational physics. Here we propose a neural-network-based solver, which enables us to cover the high-dimensional variable space for this purpose. The efficiency of the solver is analyzed by examples aimed at demonstrating the concept and various aspects of the task: the simultaneous finding of multiple excited states of lowest energies, the computation of energy-degenerate states with orthogonalized wave functions, the scalability to handle a multivariable problem, and the self-consistent determination and automatic adjustment of the imbedded Monte Carlo procedure. The solver adheres to the computational techniques developed in machine learning and is vastly different from traditional numerical methods.

DOI: 10.1103/physreva.103.032405

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