  Based on the Riesz definition of the fractional derivative the fractional
Schr\"odinger equation with an infinite well potential is investigated. First
it is shown analytically, that the solutions of the free fractional
Schr\"odinger equation are not eigenfunctions, but good approximations for
large k and in the vicinity of \alpha=2. The first lowest eigenfunctions are
then calculated numerically and an approximate analytic formula for the level
spectrum is derived.
