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On the WKB approximation for the spinless Salpeter equation

Year: 2025

Type: article

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.

Source: Results in Physics

DOI: 10.1016/j.rinp.2025.108456

Authors: Y. Chargui, S. Boulaaras, M.A.J. Mohamed

Institutions: Tunis University, Qassim University, Tunis El Manar University, Alzaiem Alazhari University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,920

OpenAlex ID: W4414568653

FWCI:

Cites: 26

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