​Scientific computing with applications to Atomic Physics Spectroscopy using several atomic computer programs in order for solving the ab-initio Non-relativistic and Relativistic Shrödinger Equation for atomic systems. From the wave-functions different properties such as energy structure, hyperfine structure, isotope shifts, transition rates, and splittings due to external magnetic fields can be determined. Solving the ab- initio Time Dependent Shrödinger Equation in application of ultrafast laser atom interactions, such as studying the non-linear response of atoms or ions in strong laser fields which leads to generate photons with ultrashort pulse duration, high brightness, and coherence called High Order Harmonics. High Order Harmonics is a unique source of XUV radiation used in several kind of laser systems​.