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Research on a new high-order generalized uncertainty principle in quantum system

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Abstract

Considering that curved space-time in coordinate or momentum representation should be curved, this paper proposes a new high-order generalized uncertainty principle by modifying the coordinate and momentum operator simultaneously, which could give a self-consistent phenomenological explanation for the existence of the minimum observable length. Moreover, using the proposed new high-order generalized uncertainty principle, we can deduce not only the minimum observable length, but also the allowable maximum observable momentum. More importantly, we further use the new generalized uncertainty principle to discuss the functional analysis of the position operator and maximum localization states, the compare the results with the existing literature. Finally, the harmonic oscillator is further discussed as an example.

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Acknowledgements

We would like to thank reviewers for their insightful comments on early drafts of this article and their comments enabled us to greatly improve the quality of our manuscript. This paper is supported by the National Natural Science Foundation of China (Grant Nos: 11465006 and 11565009) and the Major Research Project of innovative Group of Guizhou province (2018-013).

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Authors and Affiliations

  1. College of Physics, Guizhou University, Guiyang, 550025, China

    Zi-Long Zhao, Yi Yang, Hao Chen & Zheng-Wen Long

  2. College of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Qi-Kang Ran

  3. Faculty of Physics, Shahrood University of Technology, Shahrood, Iran

    Hassan Hassanabadi

Authors
  1. Zi-Long Zhao
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  2. Qi-Kang Ran
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  3. Hassan Hassanabadi
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  4. Yi Yang
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  5. Hao Chen
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  6. Zheng-Wen Long
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Correspondence to Zheng-Wen Long.

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Zhao, ZL., Ran, QK., Hassanabadi, H. et al. Research on a new high-order generalized uncertainty principle in quantum system. Eur. Phys. J. Plus 136, 293 (2021). https://doi.org/10.1140/epjp/s13360-021-01266-6

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