  We present a quantum mechanical study of the bound states of a neutral scalar
particle on the curved background described by the Reissner-Nordstr\"om (RN)
spacetime that corresponds to a naked singularity. We show that there occurs
both the metastable, \textit{i.e.} decaying bound states and the stable ones.
The corresponding energy spectra are calculated in the leading WKB
approximation and the comparison with the RN black hole quasinormal mode
spectrum is made. The metastable bound states on the naked singularity
background turn out to be more long-living than the quasinormal modes for the
black hole with the same mass.
