Abstract: In this paper, we consider convergence properties for generalized Schrödinger operators along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schrödinger operators with polynomial growth along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n \ge 1$. Secondly, we get the convergence result along a family of restricted tangential curves in $\mathbb{R} \times \mathbb{R}$. As a corollary, we obtain the sharp $L^p$-Schrödinger maximal estimates along tangential curves in $\mathbb{R} \times \mathbb{R}$.

Key words: convergence rate, tangential curve, maximal estimates