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Duffin-Kemmer-Petiau Oscillator with Spin Non-Commutativity

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Abstract

In this study, we provide the precise solution to the Duffin-Kemmer-Petiau Oscillator equation within the framework of spin non-commutativity in both one-dimensional and two-dimensional scenarios. Our methodology involves an algebraic approach that encompasses the extenion of position \(\hat{x}\) and momentum \(\hat{p}\) operators. This extension allows us to compute the energy spectrum \(E_{n}\) and the wave function \(\phi \). Notably, our finding indicate that in the one-dimensional scenario, the wave function \(\phi \)is represented using Hermite polynomials \(H_{n}\), while in the two-dimensional scenario, it is expressed through the confluent hypergeometric function \(_{1}F_{1}\left( -n,\left| l\right| +1,\frac{1}{\ m\omega } p^{2}\right) .\) We systematically examined limiting cases, particularly when \(\theta \rightarrow 0\) and \(k\rightarrow 0\). Additionally, we conducted an in-depth analysis of thermal properties (Z, U, F, C, S), representing them visually through graphs.

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Acknowledgements

We extend our sincere appreciation to the editor and reviewers for their invaluable feedback and insightful suggestions that greatly enhanced the quality of this manuscript. I extend my sincere gratitude to the esteemed editor for the diligent efforts invested in enhancing this manuscript.

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  1. Theoretical Physics and Radiation Matter Interactions Laboratory (LPTHIRM), Physics Department, Sciences Faculty, University of Saad Dahlab - Blida 1, PO box 270 Soumaa Road, 09000, Blida, Algeria

    M’hamed Hadj Moussa

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This manuscript represents the original work of a single author. The author, " M’hamed Hadj Moussa ", has contributed to all aspects of the research project and the development of this article. As the sole author of this article, I take full responsibility for its content and guarantee its accuracy and integrity. All relevant ethical guidelines and protocols were followed during the research process. I affirm that this article has not been published previously and is not under consideration for publication elsewhere. Please feel free to contact me should you have any questions or require further information. Sincerely, M’hamed Hadj Moussa Theoretical Physics and Radiation Matter Interactions Laboratory (LPTHIRM), Physics Department, Sciences Faculty , University of Saad Dahlab - Blida 1 , PO box 270 Soumaa Road , 09000 , Blida, Algeria.

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Hadj Moussa, M. Duffin-Kemmer-Petiau Oscillator with Spin Non-Commutativity. Int J Theor Phys 62, 218 (2023). https://doi.org/10.1007/s10773-023-05466-x

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