  We consider the minimally coupled Klein-Gordon equation for a charged,
massive scalar field in the non-extremal Reissner-Nordstr\"om background.
Performing a frequency domain analysis, using a continued fraction method, we
compute the frequencies \omega for quasi-bound states. We observe that, as the
extremal limit for both the background and the field is approached, the real
part of the quasi-bound states frequencies $\mathcal{R}(\omega)$ tends to the
mass of the field and the imaginary part $\mathcal{I}(\omega)$ tends to zero,
for any angular momentum quantum number $\ell$. The limiting frequencies in
this double extremal limit are shown to correspond to a distribution of
extremal scalar particles, at stationary positions, in no-force equilibrium
configurations with the background. Thus, generically, these stationary scalar
configurations are regular at the event horizon. If, on the other hand, the
distribution contains scalar particles at the horizon, the configuration
becomes irregular therein, in agreement with no hair theorems for the
corresponding Einstein-Maxwell-scalar field system.
