Factorization of the Quantum Fractional Oscillator
Mathematical Physics
2016-05-05 v1 math.MP
Quantum Physics
Abstract
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-integer differential order of the eigenvalue equation.
Cite
@article{arxiv.1605.01088,
title = {Factorization of the Quantum Fractional Oscillator},
author = {Fernando Olivar-Romero and Oscar Rosas-Ortiz},
journal= {arXiv preprint arXiv:1605.01088},
year = {2016}
}