  We study the Strichartz estimates for the magnetic Schr\"odinger equation in
dimension $n\geq3$. More specifically, for all Schr\"odinger admissible pairs
$(r,q)$, we establish the estimate
  $$
  \|e^{itH}f\|_{L^{q}_{t}(\mathbb{R}; L^{r}_{x}(\mathbb{R}^n))} \leq
C_{n,r,q,H} \|f\|_{L^2(\mathbb{R}^n)}
  $$ 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. Moreover, for the endpoint
estimate of the magnetic case in $\mathbb{R}^3$, we investigate an equivalence
  $$
  \| H^{\frac{1}{4}} f \|_{L^r(\mathbb{R}^3)} \approx C_{H,r} \big\|
(-\Delta)^{\frac{1}{4}} f \big\|_{L^r(\mathbb{R}^3)}
  $$ and find sufficient conditions on $H$ and $r$ for which the equivalence
holds.
