Numerical evaluation of energy shifts due to dipole moments interaction in a hydrogen atom

Abstract

This study aimed to numerically investigate the impact of dipole-dipole interactions on the energy levels of a hydrogen atom, specifically the energy shift caused by the interaction of the atom's dipole moment with external electric fields. This research involved applying perturbation theory and numerical techniques to quantify the changes in energy levels due to dipole orientations and magnitudes, contributing to a deeper understanding of atomic behavior and its implications in various scientific disciplines. The results presented showed that the wavefunction of the hydrogen atom exhibits degeneracy, especially n=2, n=3  states. This implies that n=2, n=3, have different states but the same energy as a result of the subshells with angular momentum l, which contains  2l+1 distinct state corresponding to positive value of m (magnetic angular momentum quantum number) m=-l±1. The total degeneracy of the energy levels n is caused by n². We find out that as the orientation of the electron charges (θ,ϕ) change the dipole moment also changes and thus has a perturbing effect on the energy levels of the hydrogen atom leading to a shift in its energy. This is confirmed, as the energy shift increases slightly from the ground state energy function Φ₁₀₀ to the second exicted state Φ₃₀₀, while the degeneracy state of Φ₃₁₀ experiences infinitesimal energy shift above. This is because the probability of the electron been found in the lower energy level is greater than at higher energy level and so it is mostly affected there by energy shift. Also, the dipole moment could increase liberational energy of the atom and thus lead to more excitement even though its impact is quite negative. The outcome of this study could have implications in precision measurements, quantum computing, and the understanding of complex atomic systems.