Abstract:  In this paper, the Gaussian expansion method is used to accurately solve the Schrodinger equation of the hydrogen atom and obtain its energy levels and wave functions. The influence of the selection of variational parameters in the Gaussian expansion method on the accuracy of the results is studied. The program is written in Python, and this method and accompanying code can be beneficial to teachers and students in teaching and learning computational physics and quantum physics.

Key words:  Gaussian expansion method, hydrogen atom energy level, hydrogen atom wave function