https://doi.org/10.1140/epjp/s13360-022-02849-7
Regular Article
Numerov and phase-integral methods for charmonium
Dipartimento di Fisica “Ettore Pancini” and INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
a
Giampiero.Esposito@na.infn.it
Received:
7
February
2022
Accepted:
18
May
2022
Published online:
30
May
2022
This paper applies the Numerov and phase-integral methods to the stationary Schrödinger 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 Schrödinger 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.
© The Author(s) 2022
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