Effects of the interaction between the magnetic moments of the proton and electron on the energy states of hydrogen atom

TL;DR

This paper investigates how the magnetic interactions between proton and electron affect hydrogen atom energy levels, comparing standard calculations with a modified Coulomb potential approach, and finds improved agreement with experimental data.

Contribution

It introduces a modified Coulomb potential accounting for magnetic interactions and compares two methods of solving the Schrödinger equation, showing the more accurate method aligns better with experiments.

Findings

Modified Coulomb potential improves energy level predictions.

Solving Schrödinger equation directly yields better results.

Taylor series expansion is less accurate.

Abstract

We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In this later method we use to ways. One is that in which we solve the Schroedinger equation with the modified Coulomb potential and some constraint conditions. The other is that in which we expand the modified Coulomb potential in Taylor series. The obtained results show that the first way gives a better agreement with experimental data.