Abstract
With the discovery of extremely high magnetic fields of about 10^6 ~ 10^9 Gauss for white dwarfs, 10^9 ~ 10^13 Gauss for neutron stars, and probably 10^14 ~ 10^15 Gauss for magnetars, the calculation of energy levels of atoms is very important for high energy astrophysics. Particularly, strong magnetic fields of neutron stars substantially modify atomic structures, energy levels, and other properties. Without calculating the structures of atoms on the surface of neutron stars, opacities due to bound-bound and bound-free processes cannot be acquired, and computed spectra are rather unrealistic. In our work, we treat a two-body problem of a hydrogen atom with a simple harmonic approximation in strong magnetic fields about 10^12, using B-splines as the basis functions of wave functions in cylindrical coordinates.Different from previous works by other authors, we start from the following two considerations: (1) the proton spreading due to strong magnetic fields is not negligible, and it leads to a significant change of the computed binding energy; (2) the center-of-mass motion and the relative motion of particles in strong magnetic fields can not be separated in a quantum mechanical view. We calculate the energy levels of low-lying states, and compare these results with other published ones. We obtain remarkable difference from others– the binding energy is much larger than others and shows that the Coulomb interaction is almost comparable with the landau level energies of electrons. However, our work is only a preliminary one. There still exist some issues to be clarified and improved in the future.