4.5 Article

Numerov and phase-integral methods for charmonium

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EUROPEAN PHYSICAL JOURNAL PLUS
卷 137, 期 5, 页码 -

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SPRINGER HEIDELBERG
DOI: 10.1140/epjp/s13360-022-02849-7

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  1. Universita degli Studi di Napoli Federico II within the CRUI-CARE Agreement

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This paper applies the Numerov and phase-integral methods to study the bound states of charm anti-charm quarks. The Numerov method always agrees with the early results of Eichten et al., while an original evaluation of the phase-integral quantization condition clarifies under which conditions the previous results on higher-order terms can be obtained.
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 the second-order ordinary differential 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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