Volume 8, Issue 3, May 2020, Page: 40-45
Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference
Yun-Sok Shin, Sejong Academy of Science and Arts, Sejong, Republic of Korea
Received: May 11, 2020;       Accepted: Jun. 2, 2020;       Published: Jun. 15, 2020
DOI: 10.11648/j.ajpa.20200803.12      View  100      Downloads  58
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.
Keywords
Tunneling, Potential Barrier, Observer Effect, Fluctuations of an Observer’s Frame of Reference, Fluctuating Frame of Reference
To cite this article
Yun-Sok Shin, Tunneling Through a One-Dimensional Square Potential Barrier Under Fluctuations in an Observer’s Frame of Reference, American Journal of Physics and Applications. Vol. 8, No. 3, 2020, pp. 40-45. doi: 10.11648/j.ajpa.20200803.12
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
L. de Broglie, “Recherches sur la théorie des quanta,” Ann. Phys., vol. 10, 1925, pp. 22–128.
[2]
E. Schrödinger, “An undulatory theory of the mechanics of atoms and molecules,” Phys. Rev., vol. 28, 1926, pp. 1049–1070.
[3]
W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Z. Phys., vol. 43, 1927, pp. 172–198.
[4]
J. Elster and H. Geitel, “Bequerel rays,” Wied. Ann., vol. 66, 1889, p. 735.
[5]
E. R. von Schweidler, Premier Congres de Radiologie, Liege, 1905.
[6]
E. Rutherford, “Radioactive substance emitted from Thorium compounds,” Phil. Mag., vol. 49, 1900, pp. 1–14.
[7]
G. Gamow, “The quantum theory of atomic nucleus,” Z. Phys., vol. 51, 1928, pp. 204–212.
[8]
R. W. Gurney and E. U. Condon, “Wave mechanics and radioactive disintegration,” Nature, vol. 122, 1928, p. 439.
[9]
G. Gamow, “The quantum theory of nuclear disintegration,” Nature, vol. 122, 1928, pp. 805–806.
[10]
R. W. Gurney and E. U. Condon, “Quantum mechanics and radioactive disintegration,” Phys. Rev., vol. 33, 1929, pp. 127–140.
[11]
C. Détraz, “The discovery of radioactivity: A one-hundred year heritage,” Nucl. Phys. A, vol. 654, 1999, pp. 12c–18c.
[12]
R. H. Fowler and L. Nordheim, “Electric emission in intense electric fields,” Proc. Roy. Soc. A, vol. 119, 1928, pp. 173–181.
[13]
L. Esaki, “Long journey into tunneling,” Proc. of the IEEE, vol. 62, 1974, pp. 825–831.
[14]
I. Giaever, “Electron tunneling and superconductivity,” Science, vol. 183, 1974, pp. 1253–1258.
[15]
B. D. Josephson, “The discovery of tunneling supercurrent,” Science, vol. 184, 1974, pp. 527–530.
[16]
P. Benioff, “The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines,” Journal of Statistical Physics, vol. 22, 1980, pp. 563–591.
[17]
Y. I. Manin, “Computable and noncomputable (in Russian),” Sov. Radio., 1980, pp. 13–15.
[18]
R. Feynman, “Simulating Physics with Computers,” International Journal of Theoretical Physics, vol. 21, 1982, pp. 467–488.
[19]
P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc., 1994, pp. 124–134.
[20]
D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A, vol. 57, 1998, pp. 120–126.
[21]
J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature, vol. 453, 2008, pp. 1031–1042.
[22]
E. Gibney, “Quantum gold rush: the private funding pouring into quantum start-ups,” Nature, vol. 574, 2019, pp. 22–24.
[23]
G Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, “Tunneling through a controllable vacuum gap,” Appl. Phys. Lett., vol. 40, 1982, pp. 178–179.
[24]
G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett., vol. 49, 1982, pp. 57–60.
[25]
G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, “7 × 7 Reconstruction on Si (111) resolved in real space,” Phys. Rev. Lett., vol. 50, 1982, pp. 120–122.
[26]
J. Tersoff and D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B, vol. 31, 1985, pp. 805–813.
[27]
M. Morgenstern, D. Haude, V. Gudmundsson, Chr. Wittneven, R. Dombrowski, Chr. Steinebach, and R. Wiesendanger, “Low temperature scanning tunneling spectroscopy on InAs (110),” Journal of Electron Spectroscopy and Related Phenomena, vol. 109, 2000, pp. 127–145.
[28]
L. J. Lauhon and W. Ho, “Direct observation of the quantum tunneling of single hydrogen atoms with a scanning tunneling microscope,” Phys. Rev. Lett., vol. 85, 2000, pp. 4566–4569.
[29]
K. Oura, V. G. Lifshits, A. A. Saranin, A. V. Zotov, and M. Katayama, Surface science: an introduction, Springer-Verlag, 2003, pp. 159–163.
[30]
Y.-S. Shin, “The average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference,” Am. J. Phys. Appl., vol. 7, 2019, pp. 21–26.
[31]
Y.-S. Shin, “Average current through a single-electron transistor with a channel under fluctuations of an observer’s frame of reference,” Am. J. Phys. Appl., vol. 7, 2019, pp. 118–124.
[32]
A. C. Phillips, Introduction to Quantum Mechanics, John Wiley & Sons Ltd., 2003, pp. 83–108.
[33]
R. A. Serway and J. W. Jewett, Physics of Scientists and Engineers with Modern Physics, 9th ed., Brooks/Cole, 2014, p. 1243.
Browse journals by subject