Abstract
In this work, the reduced spinless Salpeter equation is transformed into a relativistic second-order Schrödinger-like wave equation. The converted equation is so simple that one can solve it by using our proposed perturbation technique within the framework of the asymptotic iteration method. As an example, the Coulomb and Oscillator potential models are tested within this method. It is found that this method yields quite simple analytical solutions that will give rapidly the bound state energies with good accuracy compared with the available theoretical predictions. Furthermore, we predicted the relativistic energy eigenvalues of muonium, as well as, for the positronium bound states arising from the one-photon exchange in QED.
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08 June 2021
A Correction to this paper has been published: https://doi.org/10.1007/s13538-021-00935-2
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Acknowledgements
One of the authors (H. I. Alrebdi) extends her appreciation to the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University, where this research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program.
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The original online version of this article has been revised: Haifa I. Alrebdi’s given name was corrected.
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Barakat, T., Alrebdi, H.I. The Reduced Spinless Salpeter Wave Equation for Bound State Systems. Braz J Phys 51, 796–802 (2021). https://doi.org/10.1007/s13538-021-00874-y
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DOI: https://doi.org/10.1007/s13538-021-00874-y