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Results in Physics

On the WKB approximation for the spinless Salpeter equation

YASSINE CHARGUI, Salah Boulaaras, M.A.J. Mohamed

Published Sep 27, 2025• 0 citations
Publisher

Abstract

We extend the Wentzel–Kramers–Brillouin (WKB) approximation to the semi-relativistic spinless Salpeter equation. The Bohr–Sommerfeld quantization rule for a one-dimensional potential is derived by properly connecting the WKB wave functions. Since the latter diverges at the classical turning points (TPs), we develop a uniform WKB approach that yields an approximate wave function valid everywhere including the TPs, along with a modified quantization condition. The method is illustrated for the symmetric linear potential, and comparison with exact numerical results shows excellent agreement, significantly improving upon the standard WKB method.

DOI
10.1016/j.rinp.2025.108456

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