  We consider the linear, time-independent fractional Schr\"odinger equation $$
  (-\Delta)^s \psi+V\psi=f. $$ We are interested in the local H\"older
exponents of distributional solutions $\psi$, assuming local $L^p$
integrability of the functions $V$ and $f$. By standard arguments, we obtain
the formula $2s-N/p$ for the local H\"older exponent of $\psi$ where we take
some extra care regarding endpoint cases. For our main result, we assume that
$V$ and $f$ (but not necessarily $\psi$) are radial functions, a situation
which is commonplace in applications. We find that the regularity theory
"becomes one-dimensional" in the sense that the H\"older exponent improves from
$2s-N/p$ to $2s-1/p$ away from the origin. Similar results hold for
$\nabla\psi$ as well.
