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

Yun-Sok Shin

doi:doi:10.11648/j.ajpa.20200803.12

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

Yun-Sok Shin

Published in American Journal of Physics and Applications (Volume 8, Issue 3)

Received: 11 May 2020 Accepted: 2 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.

Published in	American Journal of Physics and Applications (Volume 8, Issue 3)
DOI	10.11648/j.ajpa.20200803.12
Page(s)	40-45
Creative Commons	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), 2020. 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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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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ACS Style

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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AMA Style

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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference
AU  - Yun-Sok Shin
Y1  - 2020/06/15
PY  - 2020
N1  - https://doi.org/10.11648/j.ajpa.20200803.12
DO  - 10.11648/j.ajpa.20200803.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 40
EP  - 45
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20200803.12
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.
VL  - 8
IS  - 3
ER  -

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Author Information

Yun-Sok Shin

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

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APA Style

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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ACS Style

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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AMA Style

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference
AU  - Yun-Sok Shin
Y1  - 2020/06/15
PY  - 2020
N1  - https://doi.org/10.11648/j.ajpa.20200803.12
DO  - 10.11648/j.ajpa.20200803.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 40
EP  - 45
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20200803.12
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.
VL  - 8
IS  - 3
ER  -

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