Physics-Informed Neural Networks as Solvers for the Time-Dependent Schr\"odinger Equation

TL;DR

This paper explores the use of physics-informed neural networks (PINNs) to solve the time-dependent Schrödinger equation, demonstrating their effectiveness in modeling quantum harmonic oscillator dynamics across different parameters.

Contribution

It introduces PINNs as a novel approach for solving the time-dependent Schrödinger equation and evaluates their performance and generalizability in quantum systems.

Findings

PINNs accurately model quantum harmonic oscillator dynamics.

PINNs show good generalization across parameters and energy states.

The method offers a flexible alternative to traditional solvers.

Abstract

We demonstrate the utility of physics-informed neural networks (PINNs) as solvers for the non-relativistic, time-dependent Schr\"odinger equation. We study the performance and generalisability of PINN solvers on the time evolution of a quantum harmonic oscillator across varying system parameters, domains, and energy states.