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

Abstract

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${p}_{\mathrm{\ensuremath{-}}1}$) 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.