  We investigate the superradiant instability of Kerr black holes under a
massive scalar perturbation. We obtain a potential $V_i(r)$ when expanding the
scalar potential $V_K(r)$ for large $r$. The Newton potential $V_1(r)$ and the
far-region potential $V_2(r)$ are used to explore the superradiant instability,
while $V_3(r)$ matches a geodesic potential $V_{gK}(r)$ for a neutral particle
moving around the Kerr black hole. Thus, $V_{gK}(r)$ is employed to fix the
separation constant. We obtain a condition for a trapping well to possess a
quasibound state in the Kerr black holes by analyzing the Newton potential
$V_1(r)$and far-region wave functions obtained from $V_2(r)$. The other
condition for no trapping well (a tiny well) is found to generate an asymptotic
bound state. Finally, we discuss an ultralight boson whose potential has a tiny
well located at asymptotic region.
