Abstract:
In this thesis, we have examined the limitations of the nonrelativistic Schrödinger equation
focusing on the study of relativistic effects in muonic hydrogen. Muonic hydrogen is an exotic
atom where a muon replaces the electron in the orbit around a nucleus. The minimal coupling
prescription has been used to incorporate the central potential into the Dirac equation, resulting
in coupled Pauli spinor equations. By applying operators for angular momentum and properties of
spherical spinors, radial Dirac equations have been derived. The study has addressed the
nonrelativistic limit and demonstrated the reduction of the Dirac equation to the Schrödinger
equation with first-order relativistic corrections, including the kinetic energy correction, spin orbit coupling, and Darwin term. Python programming language has been employed to generate
data for electronic and muonic hydrogen atoms, examining shifts in muonic hydrogen spectra due
to relativistic effects. The results have revealed that the relativistic effects are more prominent in
muonic hydrogen atom when compared to the ordinary hydrogen due to large rest mass of muon.
Moreover, the findings of this work offer insights into muonic hydrogen spectroscopy and have
implications for understanding the fine structure of atomic energy levels.
