Al-Masaeed, MohamedBaleanu, DumitruRabei, Eqab M.Al-Jamel, AhmedBaleanu, DumitruMatematik2022-12-072022-12-072021Al-Masaeed, Mohamed...et al. (2021). "Quantization of fractional harmonic oscillator using creation and annihilation operators", Open Physics, Vol. 19, No. 1, pp. 395-401.2391-5471https://doi.org/10.1515/phys-2021-0035Al-Masaeed, Mohamed/0000-0001-5647-2339In 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.eninfo:eu-repo/semantics/openAccessHarmonic OscillatorConformable DerivativeFractional Order CreationAnnihilation OperatorsArticle19139540110.1515/phys-2021-00352-s2.0-85111306316WOS:000682711700001Q3Q2