Understanding the behavior of quantum systems under external perturbations is fundamental in quantum mechanics and has numerous applications in fields such as spectroscopy and quantum computing. In this thesis, we investigate the phenomenon of Autler-Townes doublets in hydrogen atoms numerically, focusing on a three-level model. Autler-Townes doublets arise when a two-level quantum system, such as a hydrogen atom, is subjected to an external electromagnetic field, leading to the splitting of spectral lines due to the Autler-Townes effect. The study involves formulating and solving the population amplitude equations describing the time evolution of the hydrogen atom’s probability amplitudes under the influence of external fields. We employ the Range-Kutta method in MATLAB to numerically solve these equations and analyze the shape and characteristics of Autler-Townes doublets. Our simulations explore the influence of various parameters such as field strength and frequency on the doublet structure. Additionally, our research compares the numerical results obtained from the simulation with the three-level model solutions, providing insights into the dynamic interference and understanding the physical reasons for the modulations in the spectrum. Our findings not only contribute to the understanding of Autler-Townes doublets in hydrogen atoms but also shed light on potential applications in quantum technologies and spectroscopic techniques.