In this paper, we consider the following Schrödinger–Newton equation \(\begin{aligned} -\epsilon ^2\Delta u+V(x)u=\frac{u}{8\pi \epsilon ^2}\int _{\mathbb {R}^3}\frac{u^2(y)}{|x-y|}\,dy,\quad x\in \mathbb {R}^3, \end{aligned}\) where \(\epsilon >0\) is a small parameter, and V is a smooth, uniformly positive potential. Let \(\Gamma \) be a smooth, closed, stationary and nondegenerate curve with respect to the functional \(\int _{\Gamma }V^\sigma \,d\gamma \) with some \(\sigma >0\) . We establish the existence of a solution \(u_\epsilon \) concentrating along a curve near \(\Gamma \) , provided \(\epsilon \) is sufficiently small and away from specific critical values. This result first extends the Ambrosetti–Malchiodi–Ni conjecture to the context of the Schrödinger–Newton equation.
