  We study uniqueness and nondegeneracy of ground states for stationary
nonlinear Schr\"odinger equations with a focusing power-type nonlinearity and
an attractive inverse-power potential. We refine the results of Shioji and
Watanabe (2016) and apply it to prove the uniqueness and nondegeneracy of
ground states for our equations. We also discuss the orbital instability of
ground state-standing waves.
