On an approximation of the two-body spinless Salpeter equation
Physics Department, College of Science and Arts at ArRass, Qassim University, PO Box 53, 51921, ArRass, Saudi Arabia
2 Université de Tunis El Manar, Faculté des Sciences de Tunis, Unité de Recherche de Physique Nucléaire et des Hautes Energies, 2092, Tunis, Tunisia
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Accepted: 21 November 2018
Published online: 24 December 2018
In recent years several published works have aimed at finding approximate analytical solutions of the two-body spinless Salpeter equation, starting from the approximation . In this article we show that the approach they used ignores a term of the order which should in fact be retained in consonance with the assumed expansion of the kinetic term. We also demonstrate how effects of this term can be reduced in an additional potential using a proper gauge-fixing choice. For illustration, we solve the resulting equation under an exponential potential for s-states and we examine the significance of the extra term for the obtained energy eigenvalues.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018