庫倫場中相對論性向徑波動方程的高階WKB近似法

HIGHER-ORDER WKB APPROXIMATIONS FOR RELATIVISTIC RADIAL PROBLEMS IN A COULOMB FIELD

本文把向徑問題的高階WKB近似法，應用到某表現中的狄拉克一庫倫向徑方程式，及庫倫場中的克萊恩－戈登向徑方程式。要求整體WKB波動函數在原點的行為 與精確波動函數在原點的行為一致，並探討任意階WKB波動函數，吾人對上述二問題，都可得到精確能量光譜。本處的求法與庫倫場中薛勒汀格向徑方程式的精確 能譜的求法很相像。吾人對通常WKB近似法中常用的藍哲－肯伯修正及對梭摩菲勒相對論質點的古典量子理論付加以評論。

High-order WKB approximations for radial problems are applied to the Dirac-Coulomb radial equations in certain representation and to the Klein-Gordon radial equation for a Coulomb field. By requiring that the behavior of the total WKB wave function near the origin be the same as that of the exact wave function and by studying the WKB wave functions of any arbitrary orders， we obtain the exact energy spectrum for both cases in similar fashion as one obtains the exact spectrum for the Schrodinger radial equation for a Coulomb field. We also make some comments on the Langer-Kemble modification in the usual WKB approximation and on the Sommerfeld old quantum theory of a relativistic particle.