**author:
**R. Herrmann

**abstract:
**Based on the Riemann- and Caputo definition of the fractional derivative we tabulate the lowest n=31 energy levels and generated graphs of the occupation probability of the fractional quantum mechanical harmonic oscillator with a precision of 32 digits for 0.50 < \alpha < 2.00, which corresponds to the transition from U(1) to SO(3).

**reference: **Gam. Ori. Chron. Phys. (2013) **1**(1) 13-176