Factorization of the Quantum Fractional Oscillator

Quantum Fest 2015

Olivar-Romero, F.^1 ; Rosas-Ortiz, O.^1

Physics Department, Cinvestav, A.P. 14-740, México D.F

07000, Mexico^1

关键词: Eigenvalue equations;    Energy eigenvalues;    Factorization methods;    Fractional differential;    Fractional differential operators;    Fractional oscillators;    Power-law;    Quantum oscillators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/698/1/012025/pdf
DOI  :  10.1088/1742-6596/698/1/012025

来源: IOP

【 摘 要 】

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.