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arXiv · 2204.05702

High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method

Hugo D. Nogueira·Vladimir I. Korobov·Jean-Philippe Karr
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Abstract

The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The ground-state relativistic energy is obtained with an accuracy of $10^{-20}$, which represents an improvement by several orders of magnitude, and is shown to be in good agreement with results obtained from perturbation theory.Highly accurate relativistic wavefunctions are obtained, which is a first step towards nonperturbative calculations of the one-loop self-energy correction in hydrogen molecular ions.

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Hugo D. Nogueira, Vladimir I. Korobov, Jean-Philippe Karr. 2022-04-12. High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method. https://doi.org/10.1103/physreva.105.l060801

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