New Stokes’ line in WKB theory
New Stokes’ line in WKB theory
复制标题
WKB 理论中的新斯托克斯线
DOI：
10.1063/1.525467
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发表时间：
1982
影响因子：
1.3
通讯作者：
K. Roberts
中科院分区：
文献类型：
--
作者：
H. Berk;W. Nevins;K. Roberts
研究了一维任意阶微分方程和积分方程的WKB理论。先前为构建N阶微分方程、N大于或等于3或积分方程的Stokes线所陈述的规则被发现是不完整的，因为这些规则导致依赖于路径的解的渐近形式。当先前定义的斯托克斯线交叉时，可以产生新的斯托克斯线，这一论证解决了这个悖论。给出了WKB问题的一个新公式来证明新的Stokes线。利用新的Stokes线，可以证明渐近形式与路径无关。此外，提出了WKB特征值问题，并证明了全局色散关系是作用环积分的泛函。
The WKB theory for differential equations of arbitrary order or integral equations in one dimension is investigated. The rules previously stated for the construction of Stokes’ lines for Nth‐order differential equations, N⩾3, or integral equations are found to be incomplete because these rules lead to asymptotic forms of the solutions that depend on path. This paradox is resolved by the demonstration that new Stokes’ lines can arise when previously defined Stokes’ lines cross. A new formulation of the WKB problem is given to justify the new Stokes’ lines. With the new Stokes’ lines, the asymptotic forms can be shown to be independent of path. In addition, the WKB eigenvalue problem is formulated, and the global dispersion relation is shown to be a functional of loop integrals of the action.