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

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