Variational Calculation Of Hydrogen And Its Isotopic Molecular Ion Energy Levels

With the study of atom and molecule becomes more thorough, its function in lots of fields is appeared now. And with the development of the technology of experiment and the improvement of the performance of calculating machine, the high accurate calculation becomes a hotspot now. In this thesis, we review calculation of the atomic spectrum, atom and hydrogen-like molecule ion,and then analyze two methods——perturbation method and variation method——which are in common use. And we also analyze the characteristics and applicability of these two methods. With introducing the extending of variation method in high energy level, we advance to use variation method in order to calculate the energy level of hydrogen and its isotopes molecule ion. And according to Matrix Interleaving theory, we can get the possibility of this method.In this thesis, we discuss three-body systems such as hydrogen molecule ions. We choose the coordinate origin at one atom and then set up the coordinate, find the Hamiltonian of the system. And then reduce it into some basic integrals, using variational wave functions in fully correlated Hylleraas corrdinates to determine the non-linear parametersαandβ. In order to get the more complete basis sets, we can expand the dimensions of the basis sets.In this thesis, we calculate the energy of H2+ in L=0 and v=0 state, and improve the precision from 10-24 in literature to 10-29. We also calculate the energy of H2+ in L=0 , v=1 and L=1, v=1 state and D2+ in L=0, v=0 state, the results are more exactitude up to about 3~5 orders of magnitude than the results in literature we have found.