The calculation of rapidly converging lower and upper bounds to the ground-state energy, $E_g$, of hydrogenic atoms in superstrong magnetic fields ($B\gtrsim {10}^9$ G) has been an important theoretical problem for the past twenty-five years. Much effort has gone into reconciling the many different estimates for $E_g$ predicted by an assortment of techniques. On the basis of recently developed eigenvalue moment methods, a precise solution involving rapidly converging bounds to $E_g$ for arbitrary superstrong magnetic field strengths, is now possible.

• Received 5 October 1987

DOI:https://doi.org/10.1103/PhysRevLett.60.253