الفهرس 
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Abstract
In this thesis, we use the well-known quantum Monte Carlo methods to study and investigate various types of atomic and molecular ions quantum systems. Firstly, the variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom, helium like ions, and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box had calculated. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions had performed. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.