This research work attempts to address the genuine problem of Astrophysics - finding Hydrogen Column density in desired matter of interest. It encompasses research work based on ab-initio calculation and, subsequent spectral analyis. Ab-initio calculations is based on Hartree Fock level of approximation while spectral analysis is done on the spectrum of higher CO lines (J=7->6) available from NANTEN Observatory located at Alma, Chile. The study of column density of Hydrogen molecule in the core region of NGC 3603 is performed ultimately. I would like to express my sincere gratitude to my supervisors Prof. Dr. Mukunda Mani Aryal and Dr. Binil Aryal for suggesting the problem and providing constant guidance throughout this work. Working under them was a unique experience and a matter of great rejoice.