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SOLVING THE SCHRÖDINGER AND DIRAC EQUATIONS FOR A HYDROGEN ATOM IN THE UNIVERSE'S STRONGEST MAGNETIC FIELDS WITH THE FREE COMPLEMENT METHOD

The free complement method for solving the Schrödinger 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 (∼1015 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 Schrödinger and Dirac equations provides an accurate theoretical methodology for studying phenomena that occur under strong magnetic fields.