Hydrogen atom H andH2+molecule in strong magnetic fields

Abstract

The finite-elements method is used to solve, to the given degree of accuracy, bound states of the H atom and the molecular ion ${\mathrm{H}}_2^{+}$ of hydrogen in a strong magnetic field, ${10}^9$ <H <${10}^{13}$ gauss, and stronger. In the case of the hydrogen atom, the results are in agreement (within a factor of ∼ ${10}^{-4\mathrm{}}$) with results of the best variational calculations in the area of field changes, while in the case of the molecular hydrogen ion and for the 0<H <${10}^{11}$ gauss field they are far better than all calculations known to date. The opinion presented here is that the finite-elements method used in this paper—i.e., the method of direct solution of the particular problem on a plane—can also be successfully used in many other physics problems which are reduced to partial differential equations on a plane, and when perturbation theory or some other similar method of solution is not applicable.