Eigenvalue analysis by discrete variables

Abstract

Fourier grid Hamiltonian (FGH) method is applied to calculate vibrational energy levels of hydrogen molecule. Meyer's method and Balint-Kurti's method are briefly described. Difference of these methods is grid point range. Grids used in Meyer's method range from -pi to pi. On the other hand, Balint-Kurti's method uses distance L as grid range. Balint-Kurti's method with very accurate potential energies of hydrogen molecule by Pachuckis is applied to calculate vibrational energy levels of hydrogen molecule. Because of the equal grid space in the theory, 36 grid points range from 0.5 to 4.0 bohr of nuclear distances (space length is 0.1 bohr) are selected from Pachuckis's results as potential energies of FGH. Lowest 14 vibrational energy levels are calculated by FGH. Good agreement between theoretical and experimental results obtained for energy difference between vibrational energy levels from v = 0 to 10. However, beyond v=11, errors become large because of neighbor of dissociation limit.