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On the multiple internal reflections of particles and phonons tunneling in one, two, or three dimensions


Institute for Nuclear Research of National Academy of Sciences Ukraine, prosp. Nauki 47, Kiev, 30650, Ukraine

An analysis is given of multiple internal reflections undergone by particles and phonons undergoing one-, two-, and three-dimensional tunneling. Results obtained by using the time dependent Schrödinger equation for nonrelativistic particles and those obtained with the time dependent Helmholtz equation for electromagnetic waves are presented. The paper closes with conclusions and considerations for future research.

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Fulltext is also available at DOI: 10.3367/UFNe.0184.201411h.1255
PACS: 03.65.Xp, 42.25.−p, 42.50.Xa (all)
DOI: 10.3367/UFNe.0184.201411h.1255
URL: https://ufn.ru/en/articles/2014/11/g/
000349435700007
2-s2.0-84922687937
2014PhyU...57.1136O
Citation: Olkhovsky V S "On the multiple internal reflections of particles and phonons tunneling in one, two, or three dimensions" Phys. Usp. 57 1136–1145 (2014)
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Received: 10th, March 2014, revised: 15th, May 2014, 20th, May 2014

Оригинал: Ольховский В С «O многократных внутренних отражениях туннелирующих частиц и фотонов в одномерном, двухмерном и трёхмерном туннелировании» УФН 184 1255–1264 (2014); DOI: 10.3367/UFNr.0184.201411h.1255

References (66) ↓ Cited by (4) Similar articles (20)

  1. Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika (M.: Fizmatgiz, 1959); Akhiezer A I, Berestetskii V B Quantum Electrodynamics (New York: Interscience Publ., 1965)
  2. Shveber S Vvedenie v Relyativistskuyu Kvantovuyu Teoriyu Polya (M.: IL, 1963), Gl. 5.3; Schweber S S An Introduction To Relativistic Quantum Field Theory (Evanston, Ill.: Row, Peterson, 1961)
  3. Enders A, Nimtz G J. Physique I 2 1693 (1992)
  4. Enders A, Nimtz G J. Physque I 3 1089 (1993)
  5. Enders A, Nimtz G Phys. Rev. B 47 9605 (1993)
  6. Enders A, Nimtz G Phys. Rev. E 48 632 (1993)
  7. Nimtz G Tunneling And Its Implications (Eds A Ranfagni, L S Schulman) (Singapore: World Scientific, 1997) p. 223
  8. Wigner E P Phys. Rev. 98 145 (1955)
  9. Olkhovsky V S, Recami E Phys. Rep. 214 339 (1992)
  10. Olkhovsky V S, Recami E, Jakiel J Phys. Rep. 398 133 (2004)
  11. Hartman T E J. Appl. Phys. 33 3427 (1962)
  12. Bose J Ch Bose Inst. Trans. 42 (1927)
  13. Steinberg A M, Kwiat P G, Chiao R Y Phys. Rev. Lett. 71 708 (1993)
  14. Chiao R Y, Kwiat P G, Steinberg A M Sci. Am. 269 (2) 52 (1993)
  15. Spielmann Ch et al. Phys. Rev. Lett. 73 2308 (1994)
  16. Balcou Ph, Dutriaux L Phys. Rev. Lett. 78 851 (1997)
  17. Jakiel J, Olkhovsky V S, Recami E Phys. Lett. A 248 156 (1998)
  18. Laude V, Tournois P J. Opt. Soc. Am. B 16 194 (1999)
  19. Haibel A, Nimtz G, Stahlhofen A A Phys. Rev. E 63 047601 (2001)
  20. Olkhovsky V S, Recami E, Salesi G Europhys. Lett. 57 879 (2002)
  21. Olkhovsky V S, Recami E, Zaichenko A K Europhys. Lett. 70 712 (2005)
  22. Nimtz G, Enders A, Spieker H J. Physique I 4 565 (1994)
  23. Longhi S et al. Phys. Rev. E 65 046610 (2002)
  24. Chiao R Y AIP Conf. Proc. 461 3 (1999)
  25. Nimtz G AIP Conf. Proc. 461 14 (1999)
  26. Recami E AIP Conf. Proc. 461 32 (1999)
  27. Steinberg A AIP Conf. Proc. 461 36 (1999)
  28. Recami E Time’s Arrows, Quantum Measurement, and Superluminal Behavior: Intern. Conf. TAQMSB, Palazzo Serra di Cassano, Napoli, October 3 - 5, 2000 (Eds D Mugnai, A Ranfagni, L S Schulman) (Roma: Consiglio Nazionale delle Ricerche, 2001) p. 17
  29. Nimtz G, Haibel A, Vetter R-M Time’s Arrows, Quantum Measurement, and Superluminal Behavior: Intern. Conf. TAQMSB, Palazzo Serra di Cassano, Napoli, October 3 - 5, 2000 (Eds D Mugnai, A Ranfagni, L S Schulman) (Roma: Consiglio Nazionale delle Ricerche, 2001) p. 125
  30. Olkhovsky V S Time’s Arrows, Quantum Measurement, and Superluminal Behavior: Intern. Conf. TAQMSB, Palazzo Serra di Cassano, Napoli, October 3 - 5, 2000 (Eds D Mugnai, A Ranfagni, L S Schulman) (Roma: Consiglio Nazionale delle Ricerche, 2001) p. 173
  31. Nimtz G Prog. Quantum Electron. 27 417 (2003)
  32. Winful H G Phys. Rep. 436 1 (2006)
  33. Recami E J. Phys. Conf. Ser. 196 012020 (2009)
  34. Nimtz G Found. Phys. 39 1346 (2009)
  35. Shvartsburg A B, Petite G, Zuev M J. Opt. Soc. Am. B 28 2271 (2011)
  36. Aharonov Y, Erez N, Reznik B Phys. Rev. A 65 052124 (2002)
  37. Cardone F, Mignani R, Olkhovsky V S Phys. Lett. 289 279 (2001)
  38. Cardone F, Mignani R, Olkhovsky V S Mod. Phys. Lett. B 14 109 (2000)
  39. Cardone F, Mignani R, Olkhovsky V S J. Physique I 7 1211 (1997)
  40. Fermor J H Am. J. Phys. 34 1168 (1966)
  41. McVoy K W, Heller L, Bolsterli M Rev. Mod. Phys. 39 245 (1967)
  42. Anderson A Am. J. Phys. 57 230 (1989)
  43. Maidanyuk S P, Olkhovsky V S, Zaichenko A K J. Phys. Studies 6 (1) 24 (2002)
  44. Cardone F, Maidanyuk S P, Mignani R, Olkhovsky V S Found. Phys. Lett. 19 441 (2006)
  45. Barbero A P L, Hernández-Figueroa H E, Recami E Phys. Rev. E 62 8628 (2000)
  46. Olkhovsky V S, Romaniuk M V J. Mod. Phys. 2 1166 (2011)
  47. Steinberg A M, Chiao R Y Phys. Rev. A 49 3283 (1994)
  48. Carniglia C K, Mandel L J. Opt. Soc. Am. 61 1035 (1971)
  49. Zhu S et al. Am. J. Phys. 54 601 (1986)
  50. Olkhovsky V S et al. Central Eur. J. Phys. 6 122 (2008)
  51. Olkhovsky V S, Romaniuk M V Nucl. Phys. Atom. Energy 10 273 (2009)
  52. Olkhovsky V S Int. J. Mod. Phys. E 23 1460006 (2014); Olkhovsky V S "About the similarity of particle and photon tunneling and multiple internal reflections in 1-dimensional, 2-dimensional and 3-dimensional photon tunneling" Materiály IX Mezinárodni Vëdecko-praktická Konf. "Zprávy Vědeckeacute; Ideje", 27 Řjnřá - 05 Listopadu 2013 Roku, Fyzika, Praha (Praha: Publ. House Education and Science, 2013) p. 43
  53. Davidovskii V V, Zaichenko A L, Ol’khovskii V S Yadernaya Fizika. Sb. Nauch. Tr. In-ta Yadernykh Issled. (1(14)) 28 (2005)
  54. Preston M A Physics Of The Nucleus (Reading, Mass.: Addison-Wesley Publ. Co., 1962)
  55. Kadmenskii S G, Furman V I Al’fa-raspad i Rodstvennye Yadernye Reaktsii (M.: Energoatomizdat, 1985)
  56. Baz’ A I, Zel’dovich Ya B, Perelomov A M Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike (M.: Nauka, 1971); Baz’ A I, Zel’dovich Ya B, Perelomov A M Scattering, Reactions And Decay In Nonrelativistic Quantum Mechanics (Jerusalem: Israel Program for Scientific Translations, 1969)
  57. Baz’ A I, Gol’danskii V I, Zel’dovich Ya B Usp. Fiz. Nauk 85 445 (1965); Baz’ A I, Gol’danskii V I, Zel’dovich Ya B Sov. Phys. Usp. 8 177 (1965)
  58. Gamow G Z. Phys. 51 204 (1928)
  59. Gurney R W, Condon E D W U Nature 122 439 (1928)
  60. Gamov G A Usp. Fiz. Nauk 163 (4) 51 (1993); Gamov G A Phys. Usp. 36 (4) 267 (1993); Gamov G A Usp. Fiz. Nauk 10 531 (1930); Gamov G A Usp. Fiz. Nauk 13 46 (1933)
  61. Landau L D, Smorodinskii Ya A Lektsii Po Teorii Atomnogo Yadra (M.: Gostekhizdat, 1955); Landau L D, Smorodinsky Ya Lectures On Nuclear Theory (New York: Dover Publ., 1993)
  62. Bonetti R et al. Phys. Rev. Lett. 82 5205 (1999)
  63. Spitaleri C et al. Phys. Rev. C 63 055801 (2001)
  64. Junghans A R et al. Phys. Rev. Lett. 88 041101 (2002)
  65. Imbriani G et al. Eur. Phys. J. A 25 455 (2005)
  66. Lemut A et al. (LUNA Collab.) Phys. Lett. B 634 483 (2006)
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