In this thesis, eigenenergies and eigenfunctions of three confined quantum systems: Hydrogen atom in spherical cavity, Hydrogen atom in ellipsoidal cavity and H 2 + in ellipsoidal cavity, have been calculated using linear variational method. B-splines have been used as basis functions, which can easily construct the trial wave functions with appropriate boundary and cusp conditions. The main characteristics of B-spline are its high localization and its flexibility. Model has been used to solve this problems is that, instead of considering effects of confinement on a system, we suppose that each particle in the system is located at a confining cavity and with increasing confinement, cavity volume decreases. Accurate results obtained for hydrogen atom in spherical cavity, but about two other systems, we encountered with mathematical problems in numerical calculations and the results don't have good accuracy. Nevertheless, these results are suitable for investigation general properties of the systems. Key Words Confined quantum system, B-spline, Hydrogen atom, H 2 + molecule , Variational method .
