Factorization of the Riesz-Feller fractional quantum harmonic oscillators
| Autor: | Rosu, Haret C., Mancas, Stefan C. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | J. Phys. Conf. Series 1540, 012005 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/1540/1/012005 |
| Popis: | 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 Levy indices is briefly introduced Comment: 13 pages, 4 figures, 11 references |
| Databáze: | arXiv |
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