Uniqueness and nondegeneracy of ground states for the Schrödinger-Newton equation with power nonlinearity

In this article, we study the Schrödinger-Newton equation \begin{equation} -Δu+λu=\frac{1}{4π}\left(\frac{1}{|x|}\star u^{2}\right)u+|u|^{q-2}u \quad $\text{in}$~$\mathbb{R}$^3, \end{equation} where $\lambda \in {\mathbb{R}}_{+}$, $q\in (2,3)\cup (3,6)$. By investigating limit profiles of ground states as $\lambda \to 0^{+}$ or $\lambda \to +\mathrm{\infty }$, we prove the uniqueness of ground states. By the action of the linearized eqaution with respect to decomposition into spherical harmonics, we obtain the nondegeneracy of ground states.