Factorization of the Quantum Fractional Oscillator

@article{OlivarRomero2016FactorizationOT,
  title={Factorization of the Quantum Fractional Oscillator},
  author={Fernando Olivar-Romero and Oscar Rosas‐Ortiz},
  journal={Journal of Physics: Conference Series},
  year={2016},
  volume={698}
}
The applicability of the factorization method is extended to the case of quantum fractional-differential Hamiltonians. In contrast with the conventional factorization, it is shown that the ‘factorization energy’ is now a fractional-differential operator rather than a constant. As a first example, the energies and wave-functions of a fractional version of the quantum oscillator are determined. Interestingly, the energy eigenvalues are expressed as power-laws of the momentum in terms of the non… 

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