$Quantization of fractional harmonic oscillator using creation and annihilation operators$
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Quantization of fractional harmonic oscillator using creation and annihilation operators

In this article, the Hamiltonian for the conformable 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-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fr...

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Autores principales:	Al-Masaeed Mohamed, Rabei Eqab. M., Al-Jamel Ahmed, Baleanu Dumitru
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	harmonic oscillator conformable derivative fractional order creation annihilation operators Physics QC1-999
Acceso en línea:	https://doaj.org/article/4a1ee8df6a8c43b088388af86b48a6ae
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id	oai:doaj.org-article:4a1ee8df6a8c43b088388af86b48a6ae
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spelling	oai:doaj.org-article:4a1ee8df6a8c43b088388af86b48a6ae2021-12-05T14:11:02ZQuantization of fractional harmonic oscillator using creation and annihilation operators2391-547110.1515/phys-2021-0035https://doaj.org/article/4a1ee8df6a8c43b088388af86b48a6ae2021-07-01T00:00:00Zhttps://doi.org/10.1515/phys-2021-0035https://doaj.org/toc/2391-5471In this article, the Hamiltonian for the conformable 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-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fractional operators that we called α\alpha -creation and α\alpha -annihilation operators. It is found that these operators have the following influence on the energy states. For a given order α\alpha , the α\alpha -creation operator promotes the state while the α\alpha -annihilation operator demotes the state. The system is then quantized using these creation and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite functions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting α=1\alpha =1.Al-Masaeed MohamedRabei Eqab. M.Al-Jamel AhmedBaleanu DumitruDe Gruyterarticleharmonic oscillatorconformable derivativefractional order creationannihilation operatorsPhysicsQC1-999ENOpen Physics, Vol 19, Iss 1, Pp 395-401 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	harmonic oscillator conformable derivative fractional order creation annihilation operators Physics QC1-999
spellingShingle	harmonic oscillator conformable derivative fractional order creation annihilation operators Physics QC1-999 Al-Masaeed Mohamed Rabei Eqab. M. Al-Jamel Ahmed Baleanu Dumitru Quantization of fractional harmonic oscillator using creation and annihilation operators
description	In this article, the Hamiltonian for the conformable 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-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fractional operators that we called α\alpha -creation and α\alpha -annihilation operators. It is found that these operators have the following influence on the energy states. For a given order α\alpha , the α\alpha -creation operator promotes the state while the α\alpha -annihilation operator demotes the state. The system is then quantized using these creation and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite functions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting α=1\alpha =1.
format	article
author	Al-Masaeed Mohamed Rabei Eqab. M. Al-Jamel Ahmed Baleanu Dumitru
author_facet	Al-Masaeed Mohamed Rabei Eqab. M. Al-Jamel Ahmed Baleanu Dumitru
author_sort	Al-Masaeed Mohamed
title	Quantization of fractional harmonic oscillator using creation and annihilation operators
title_short	Quantization of fractional harmonic oscillator using creation and annihilation operators
title_full	Quantization of fractional harmonic oscillator using creation and annihilation operators
title_fullStr	Quantization of fractional harmonic oscillator using creation and annihilation operators
title_full_unstemmed	Quantization of fractional harmonic oscillator using creation and annihilation operators
title_sort	quantization of fractional harmonic oscillator using creation and annihilation operators
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/4a1ee8df6a8c43b088388af86b48a6ae
work_keys_str_mv	AT almasaeedmohamed quantizationoffractionalharmonicoscillatorusingcreationandannihilationoperators AT rabeieqabm quantizationoffractionalharmonicoscillatorusingcreationandannihilationoperators AT aljamelahmed quantizationoffractionalharmonicoscillatorusingcreationandannihilationoperators AT baleanudumitru quantizationoffractionalharmonicoscillatorusingcreationandannihilationoperators
_version_	1718371472146169856

Quantization of fractional harmonic oscillator using creation and annihilation operators

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