  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.
