On the WKB approximation for the spinless Salpeter equation

IF 4.6 2区物理与天体物理 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Results in Physics Pub Date : 2025-09-26 DOI:10.1016/j.rinp.2025.108456

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

引用次数: 0

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.

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无自旋Salpeter方程的WKB近似

我们把wentzel - kramer - brillouin （WKB）近似推广到半相对论的无自旋Salpeter方程。通过适当地连接WKB波函数，导出了一维势的Bohr-Sommerfeld量子化规则。由于后者在经典拐点（TPs）处发散，我们开发了一种统一的WKB方法，该方法产生了包括TPs在内的任何地方都有效的近似波函数，以及修改的量化条件。该方法对对称线性势进行了说明，并与精确数值结果进行了比较，结果吻合良好，大大改进了标准WKB方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Results in Physics MATERIALS SCIENCE, MULTIDISCIPLINARYPHYSIC-PHYSICS, MULTIDISCIPLINARY

CiteScore

8.70

自引率

9.40%

发文量

754

审稿时长

50 days

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