Abstract
The free complement method for solving the Schr¨ odinger and Dirac equations has been applied to the hydrogen atom in extremely strong magnetic fields. For very strong fields such as those observed on the surfaces of white dwarf and neutron stars, we calculate the highly accurate non-relativistic and relativistic energies of the hydrogen atom. We extended the calculations up to field strengths that exceed the strongest magnetic field (∼10 15 G) ever observed in the universe on a magnetar surface. These are the first reported accurate quantum mechanical calculations ever to include such strong fields. Certain excited state bands in extremely strong fields showed perfect diamagnetism with an infinite number of degenerate states with the same energies as for a hydrogen atom in the absence of a field. Our method of solving the Schr¨ odinger and Dirac equations provides an accurate theoretical
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