American Journal of Physics and Applications

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Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference

Received: 11 May 2020    Accepted: 02 June 2020    Published: 15 June 2020
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Abstract

This study reports tunneling through a one-dimensional (1D) square potential barrier (SPB) under fluctuations in an observer’s frame of reference (OFR). To date, tunneling through an SPB has been studied under the assumption that the OFR remains constant throughout the tunneling measurements; therefore, the change of the tunneling probability when the OFR is assumed to fluctuate remains unanswered. In this paper, a 1D SPB is considered under fluctuations of an OFR. The average transmission probability of a particle through an SBP for two types of OFR fluctuations (periodic-square-wave and periodic-sawtooth-wave fluctuations) is formulated in time representations. Under these types of fluctuations, the average transmission probability gradually increases with a particle’s energy, which is saturated to the transmission probability in the case of the stationary OFR at a much greater energy than the amplitude of the fluctuations. The average transmission probability is much higher at the amplitude of the fluctuations in the case of periodic-square-wave fluctuations. Therefore, the average transmission probability with a particle’s energy has the potential to reveal the distribution of OFR fluctuations.

DOI 10.11648/j.ajpa.20200803.12
Published in American Journal of Physics and Applications (Volume 8, Issue 3, May 2020)
Page(s) 40-45
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Tunneling, Potential Barrier, Observer Effect, Fluctuations of an Observer’s Frame of Reference, Fluctuating Frame of Reference

References
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  • Sejong Academy of Science and Arts, Sejong, Republic of Korea

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    Yun-Sok Shin. (2020). Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference. American Journal of Physics and Applications, 8(3), 40-45. https://doi.org/10.11648/j.ajpa.20200803.12

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    Yun-Sok Shin. Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference. Am. J. Phys. Appl. 2020, 8(3), 40-45. doi: 10.11648/j.ajpa.20200803.12

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    Yun-Sok Shin. Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference. Am J Phys Appl. 2020;8(3):40-45. doi: 10.11648/j.ajpa.20200803.12

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  • @article{10.11648/j.ajpa.20200803.12,
      author = {Yun-Sok Shin},
      title = {Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference},
      journal = {American Journal of Physics and Applications},
      volume = {8},
      number = {3},
      pages = {40-45},
      doi = {10.11648/j.ajpa.20200803.12},
      url = {https://doi.org/10.11648/j.ajpa.20200803.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpa.20200803.12},
      abstract = {This study reports tunneling through a one-dimensional (1D) square potential barrier (SPB) under fluctuations in an observer’s frame of reference (OFR). To date, tunneling through an SPB has been studied under the assumption that the OFR remains constant throughout the tunneling measurements; therefore, the change of the tunneling probability when the OFR is assumed to fluctuate remains unanswered. In this paper, a 1D SPB is considered under fluctuations of an OFR. The average transmission probability of a particle through an SBP for two types of OFR fluctuations (periodic-square-wave and periodic-sawtooth-wave fluctuations) is formulated in time representations. Under these types of fluctuations, the average transmission probability gradually increases with a particle’s energy, which is saturated to the transmission probability in the case of the stationary OFR at a much greater energy than the amplitude of the fluctuations. The average transmission probability is much higher at the amplitude of the fluctuations in the case of periodic-square-wave fluctuations. Therefore, the average transmission probability with a particle’s energy has the potential to reveal the distribution of OFR fluctuations.},
     year = {2020}
    }
    

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    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
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    AB  - This study reports tunneling through a one-dimensional (1D) square potential barrier (SPB) under fluctuations in an observer’s frame of reference (OFR). To date, tunneling through an SPB has been studied under the assumption that the OFR remains constant throughout the tunneling measurements; therefore, the change of the tunneling probability when the OFR is assumed to fluctuate remains unanswered. In this paper, a 1D SPB is considered under fluctuations of an OFR. The average transmission probability of a particle through an SBP for two types of OFR fluctuations (periodic-square-wave and periodic-sawtooth-wave fluctuations) is formulated in time representations. Under these types of fluctuations, the average transmission probability gradually increases with a particle’s energy, which is saturated to the transmission probability in the case of the stationary OFR at a much greater energy than the amplitude of the fluctuations. The average transmission probability is much higher at the amplitude of the fluctuations in the case of periodic-square-wave fluctuations. Therefore, the average transmission probability with a particle’s energy has the potential to reveal the distribution of OFR fluctuations.
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