Article
Factorization of the Riesz-Feller Fractional Quantum Harmonic Oscillators
Quantum Fest. Journal of Physics: Conference Series.
(2020)
Abstract
Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the non-Hermitian fractional eigenvalue problem in the k space by introducing in that space a new class of Hermite 'polynomials' that we call Riesz-Feller Hermite 'polynomials'. Using the inverse Fourier transform in Mathematica, interesting analytic results for the same eigenvalue problem in the x space are also obtained. Additionally, a more general factorization with two different Lévy indices is briefly introduced.
Disciplines
Publication Date
Summer June, 2020
DOI
10.1088/1742-6596/1540/1/012005
Citation Information
Haret C. Rosu and Stefan C. Mancas. "Factorization of the Riesz-Feller Fractional Quantum Harmonic Oscillators" Quantum Fest. Journal of Physics: Conference Series. (2020) Available at: http://works.bepress.com/stefani_mancas/29/