Numerical solution of the Schrödinger equation for radiation-matter interaction models using the Runge-Kutta method implemented in Python
DOI:
https://doi.org/10.31349/RevMexFisE.23.020202Keywords:
Schrödinger equation, radiation-matter interaction, Runge-Kutta method, Jaynes-Cummings model, PythonAbstract
Obtaining exact solutions to the time-dependent Schrodinger equation in complex quantum systems presents significant challenges. In this ¨ context, numerical methods offer powerful alternatives for exploring their dynamics. In this pedagogical article, we present a numerical approach based on the fourth-order Runge-Kutta method, implemented in Python, to simulate radiation-matter interaction models. The methodology is illustrated using the well-known Jaynes-Cummings model, and the numerical results are compared with its exact analytical solution for illustrative purposes. Although only this model is explicitly solved, the numerical framework is general and can be readily extended to more complex Hamiltonians, including time-dependent cases. This makes the approach a practical and accessible tool for exploring a wide range of quantum systems.
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Copyright (c) 2026 L. Hernández-Sánchez, A. Flores-Rosas, I. Ramos-Prieto, F. Soto-Eguibar, H. M. Moya-Cessa
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