  A number of papers over the past eight years have claimed to solve the
fractional Schr\"{o}dinger equation for systems ranging from the
one-dimensional infinite square well to the Coulomb potential to
one-dimensional scattering with a rectangular barrier. However, some of the
claimed solutions ignore the fact that the fractional diffusion operator is
inherently nonlocal, preventing the fractional Schr\"{o}dinger equation from
being solved in the usual piecewise fashion. We focus on the one-dimensional
infinite square well and show that the purported groundstate, which is based on
a piecewise approach, is definitely not a solution of the fractional
Schr\"{o}dinger equation for general fractional parameters $\alpha$. On a more
positive note, we present a solution to the fractional Schr\"{o}dinger equation
for the one-dimensional harmonic oscillator with $\alpha=1$.
