Based on the Riesz definition of the fractional derivative the fractional Schroedinger equation with an infinite well potential is investigated. First it is shown analytically, that the solutions of the free fractional Schroedinger equation are not eigenfunctions, but good approximations for large k and for $\alpha \approx 2$. The first lowest eigenfunctions are then calculated numerically and an approximate analytic formula for the level spectrum is derived.
download: arxiv: arXiv:1210.4410[math-ph]
reference: Gam. Ori. Chron. Phys. (2013) 1(1) 1-12