The fractional Schr\"odinger equation and the infinite potential well - numerical results using the Riesz derivative

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.