Applications of the Numerov method to simple quantum systems using Python

TL;DR

This paper demonstrates how to implement Numerov's method in Python to solve quantum systems like the hydrogen atom, Morse potential molecules, and quantum dots, providing educational code examples.

Contribution

It offers a didactic Python implementation of Numerov's method applied to multiple quantum systems, with complete code and adaptable examples.

Findings

Successful calculation of eigenfunctions and eigenvalues for hydrogen atom

Adaptable code for Morse potential and quantum dot systems

Educational resource for numerical quantum physics methods

Abstract

Numerov's numerical method is developed in a didactic way by using Python in its {\it Jupyter Notebook} version 6.0.3 for three different quantum physical systems: the hydrogen atom, a molecule governed by the Morse potential and for a quantum dot. After a brief introduction to the Numerov method, the complete code to calculate the eigenfunctions and eigenvalues of the hydrogen atom is presented. The necessary code changes to calculate the other two examples are also provided in the sequel.