Solving the Dirac equation in central potential for muonic hydrogen atom with point-like nucleus

Abstract Muon has properties very similar to an electron. For this reason, it is possible to replace one of the electrons in an atom by a muon to form a muonic atom. The main purpose of this study is to calculate the energy eigenvalues and to study the probability density of muonic hydrogen with point like nucleus. Numerical results have generated using Matlab software programming language. The reduced mass of muon has been used in order to correct the error incurred by the assumption that the nucleus of muonic hydrogen is point-like which in turn gives it an infinite mass. The energy eigenvalues for different states have been calculated using the rest and reduced masses of muon, and the result have been tabulated. According to these results, the relativistic quantum description is not responsible for the lamb shift. The Probability density shows that muon is much more likely to be found near the nucleus of hydrogen atom for the ground state when compared with the excited states.