Hydrogen molecular ion in a strong parallel magnetic field

Abstract

The hydrogen molecular ion in a strong external magnetic field parallel to the molecular axis is investigated using a semianalytical method based on the presentation of the wave function in the form of a double power series in nonseparable space variables. The solution is determined from the requirement for the coefficients of the series to obey linear relations imposed by the Schr\"odinger equation. For the ground state, the method provides accuracy ${10}^{\mathrm{\ensuremath{-}}8}$ hartree and higher for magnetic fields from 0 up to ${10}^{4}$ T; the applicability of the technique to excited states is limited to lower field strengths.