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More specifically, for all Schr\\\"odinger admissible pairs $(r,q)$, we establish the estimate\n  $$\n  \\|e^{itH}f\\|_{L^{q}_{t}(\\mathbb{R}; L^{r}_{x}(\\mathbb{R}^n))} \\leq C_{n,r,q,H} \\|f\\|_{L^2(\\mathbb{R}^n)}\n  $$ when the operator $H= -\\Delta_A +V$ satisfies suitable conditions. In the purely electric case $A\\equiv0$, we extend the class of potentials $V$ to the Fefferman-Phong class. In doing so, we apply a weighted estimate for the Schr\\\"odinger equation developed by Ruiz and Vega. 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