粲偶素的数值积分和相积分方法
Numerov and phase-integral methods for charmonium
摘要：
本文将Numerov方法和相位积分方法应用于定态薛定谔方程，研究了粲反粲夸克的束缚态。前者是一种数值方法，非常适合于矩阵形式的二阶常微分方程，并可以适用于任何时候的定态容许泰勒级数展开。后者是一种分析方法，提供，在原则上，甚至精确的解决方案的固定薛定谔方程，以及适用于匹配的渐近展开和高阶量子化条件。Numerov方法被发现总是与Eichten等人的早期结果一致，而相位积分量化条件的原始评估阐明了在哪些条件下可以获得关于高阶项的文献中的先前结果。
英文摘要：
This paper applies the Numerov and phase-integral methods to the stationary Schrodinger equation that studies bound states of charm anti-charm quarks. The former is a numerical method well suited for a matrix form of second-order ordinary di erential equations, and can be applied whenever the stationary states admit a Taylor-series expansion. The latter is an analytic method that provides, in principle, even exact solutions of the stationary Schrodinger equation, and well suited for applying matched asymptotic expansions and higher order quantization conditions. The Numerov method is found to be always in agreement with the early results of Eichten et al., whereas an original evaluation of the phase-integral quantization condition clarifies under which conditions the previous results in the literature on higher-order terms can be obtained.
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