Numerical study of the radiation-matter interaction quantum systems through the time-dependent Schr\"odinger dynamics

TL;DR

This paper introduces a Python-based numerical method using the fourth-order Runge-Kutta algorithm to simulate radiation-matter interactions in quantum systems, validated against analytical solutions for accuracy.

Contribution

It presents a versatile numerical approach applicable to complex Hamiltonians like the Jaynes-Cummings model, enhancing analysis of quantum systems without exact solutions.

Findings

Numerical results closely match analytical solutions in test cases.

The method effectively models radiation-matter interactions in complex quantum systems.

Python implementation demonstrates accessibility and ease of use.

Abstract

Obtaining exact solutions to the Schr\"odinger equation in complex quantum systems poses significant challenges. In this context, numerical methods emerge as valuable tools for analyzing such systems. This article proposes a numerical approach using the fourth-order Runge-Kutta method, implemented in Python, to tackle radiation-matter interaction systems. This methodology is applicable to various Hamiltonians, including that of the Jaynes-Cummings model. The accuracy of the numerical results is validated by comparing them with analytical solutions in simplified cases, demonstrating its effectiveness in studying quantum systems where exact solutions cannot be derived.