Browsing by Author "Al-Masaeed, Mohamed"

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Citation - WoS: 10
Citation - Scopus: 15
Extension of Perturbation Theory To Quantum Systems With Conformable Derivative
(World Scientific Publ Co Pte Ltd, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, Mohamed
In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order alpha. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required alpha-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when alpha = 1.
Citation - WoS: 9
Citation - Scopus: 13
Quantization of Fractional Harmonic Oscillator Using Creation and Annihilation Operators
(de Gruyter Poland Sp Z O O, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, Mohamed
In this article, the Hamiltonian for the conform-able harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechan-ical operators. Math Method Appl Sci. 2020;43(11):6950-67.] is written in terms of fractional operators that we called alpha-creation and alpha-annihilation operators. It is found that these operators have the following influence on the energy states. For a given order alpha, the alpha-creation operator pro-motes the state while the alpha-annihilation operator demotes the state. The system is then quantized using these crea-tion and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite func-tions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting alpha = 1.