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The calculation of rapidly converging lower and upper bounds to the ground-state energy, E g , of hydrogenic atoms in superstrong magnetic fields (B^\0 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.

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