Finite-element calculation of low-lying states of hydrogen in a superstrong magnetic field

The finite-element method has been applied to the problem of hydrogen in a superstrong magnetic field. Binding energies have been calculated for the low-lying states (1$s_0$, 2$s_0$, 2$p_0$, and 2$p_{\mathrm{-}1}$) for a range of magnetic fields from ${10}^5$ to ${10}^{12}$ G. This calculation establishes highly accurate lower bounds for the binding energy of the excited states.