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Time in Quantum Mechanics pp 29–68Cite as

Characteristic Times in One-Dimensional Scattering

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Part of the book series: Lecture Notes in Physics ((LNPMGR,volume 72))

Abstract

Quantum scattering theory deals with collisions, namely, interactions which are essentially localized in time and space. This means that the interaction potential must vanish rapidly enough in coordinate space, so that the wave packet tends to free-motion incoming and outgoing asymptotic states before and after the interaction is effective. The scope of scattering theory also includes “half-collisions” or “decay processes” where the stage before the collision is ignored, i.e., the evolution of the system is only considered from the interaction region.

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References

  1. A.H. Zewail: Femtochemistry (World Scientific, Singapore 1994)

    Google Scholar 

  2. R.F. Snider: J. Stat. Phys. 61, 443 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  3. G. Bastard: Wave mechanics applied to semiconductor heterostructures (Les Editions de Physique, Paris 1988)

    Google Scholar 

  4. Y.B. By, S. Efrima: Phys. Rev. B 28, 4126 (1983)

    Article  ADS  Google Scholar 

  5. R.D. Levine: Quantum Mechanics of Molecular Rate Processes (Oxford University Press, Oxford 1969)

    MATH  Google Scholar 

  6. P. Deift, E. Trubowitz: Commun. Pure Appl. Math. 32, 121 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  7. A.D. Baute, I.L. Egusquiza, J.G. Muga: Int. J. Theor. Phys. Group Theor. and Nonl. Optics (2002), accepted. quant-ph/0007079

    Google Scholar 

  8. A.D. Baute, I.L. Egusquiza, J.G. Muga: J. Phys. A 34, 5341 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  9. R.F. Snider: J. Chem. Phys. 88, 6438 (1988)

    Article  ADS  Google Scholar 

  10. J.R. Tayor: Scattering Theory (John Wiley, New York 1972)

    Google Scholar 

  11. B. Diu: Eur. Phys. Lett. 1, 231 (1980)

    Google Scholar 

  12. M.S. Marinov, B. Segev: J. Phys. A: Math. Gen 29, 2839 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. J.G. Muga, S. Brouard, R. Sala: Phys. Lett. A 167, 24 (1992)

    Article  ADS  Google Scholar 

  14. M. Büttiker: Phys. Rev. B. 27, 6178 (1983)

    Article  ADS  Google Scholar 

  15. M.L. Goldberger, K.M. Watson: Collision Theory (Krieger, Huntington 1975)

    Google Scholar 

  16. H. Ekstein, A.J.F. Siegert: Ann. Phys. 68, 509 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  17. P. Exner: Open Quantum Systems and Feynman Integrals (Reidel, Dordrecht, 1985)

    MATH  Google Scholar 

  18. D. Sokolovski, J.N.L. Connor: Phys. Rev. A 44, 1500 1992)

    Article  ADS  Google Scholar 

  19. C.R. Leavens, G. Aers: in Scanning tunneling microscopy III. ed. by R. Wiesendanger, H.J. Günterodt (Springer, Berlin 1993) pp. 105–140

    Google Scholar 

  20. W. Jaworski, D. Wardlaw: Phys. Rev. A 40, 6210 (1989)

    Article  ADS  Google Scholar 

  21. H. Mizuta, T. Tanoue: The Physics y Applications de Resonant Tunnelling Diodes (Cambridge University Press, Cambridge 1995)

    Book  Google Scholar 

  22. M. Tsuchiya, T. Matsusue, H. Sakaki: Phys. Rev. Lett. 59, 2356 (1987)

    Article  ADS  Google Scholar 

  23. W. Jaworski, D.M. Wardlaw: Phys. Rev. A 37, 2843 (1987)

    Article  ADS  Google Scholar 

  24. G.R. Allcock: Ann. Phys. 53, 311 (1969)

    Article  ADS  Google Scholar 

  25. A.J. Bracken, G.F. Melloy: J. Phys. A 27, 2197 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. J.G. Muga, J.P. Palao, C.R. Leavens: Phys. Lett. A 253, 21 (1999)

    Article  ADS  Google Scholar 

  27. J.G. Muga, C.R. Leavens: Phys. Rep. 338, 353 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  28. J.G. Muga, S. Brouard, D. Macías: Annals de Physics (NY) 240, 351 (1995)

    Article  ADS  Google Scholar 

  29. S. Brouard, R. Sala, J. G. Muga: Phys. Rev. A 49, 4312 (1994)

    Article  ADS  Google Scholar 

  30. V.S. Olkhovsky, E. Recami: Phys. Rep. 214, 339 (1992)

    Article  ADS  Google Scholar 

  31. V. Delgado, S. Brouard, J.G. Muga: Solid State Comm. 94, 979 (1995)

    Article  ADS  Google Scholar 

  32. J.P. Palao, J.G. Muga, S. Brouard, A. Jadcyk: Phys. Lett. A 233, 227 (1997)

    Article  ADS  Google Scholar 

  33. R. Leavens: Physics Lett. A, 178, 27 (1993)

    Article  ADS  Google Scholar 

  34. A.M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995); Phys. Rev. A 52, 32 (1995)

    Article  ADS  Google Scholar 

  35. R.G. Newton: J. Math. Phys. 21, 493 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. C.R. Leavens, G.C. Aers: Phys. Rev. B 39, 1202 (1989)

    Article  ADS  Google Scholar 

  37. E.H. Hauge, J.A. Stovneng: Rev. Mod. Phys. 61, 917 (1989)

    Article  ADS  Google Scholar 

  38. T.E. Hartman: J. Appl. Phys. 33, 3427 (1962)

    Article  ADS  Google Scholar 

  39. J.R. Fletcher: J. Phys. C: Solid State Phys. 18, L55 (1985)

    Article  ADS  Google Scholar 

  40. F.E. Low, P.F. Mende: Ann. Phys. (NY) 210, 380 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  41. V. Delgado, J.G. Muga: Ann. Phys. (NY) 248, 122 (1996)

    Article  ADS  Google Scholar 

  42. L. Eisenbud: dissertation, Princeton Univ., June 1948 (unpublished)

    Google Scholar 

  43. F.T. Smith: Phys. Rev 118, 349 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  44. M. Sassoli de Bianchi: Helv. Phys. Acta 66, 361 (1993)

    MATH  MathSciNet  Google Scholar 

  45. H.M. Nussenzveig: Phys. Rev. 62, 042107 (2000)

    Article  ADS  Google Scholar 

  46. A. Kuppermann, J. Kaye: J. Phys. Chem. 85, 1969 (1981)

    Article  Google Scholar 

  47. R. Golub, S. Felber, R. Gähler, E. Gutsmiedl: Phys. Lett. A 148, 27 (1990)

    Article  ADS  Google Scholar 

  48. F. Goldrich, E.P. Wigner: in Magic without Magic: John Archibald Wheeler. ed. by J. R. Klauder (W. H. Freeman, San Francisco 1972) p. 147

    Google Scholar 

  49. J.G. Muga, D.M. Wardlaw: Phys. Rev. E 51, 5377 (1995)

    Article  ADS  Google Scholar 

  50. L.N. Pandey, D. Sahu, T.F. George: Appl. Phys. Lett. 56, 277 (1990)

    Article  ADS  Google Scholar 

  51. J.M. Jauch, K.B. Sinha, B.N. Misra: Helv. Phys. Acta 45, 398 (1972); T.Y. Tsang, T.A. Osborn: Nucl. Phys. A 247, 43 (1975); P. Brumer, D.E. Fitz, D. Wardlaw: J. Chem. Phys. 72, 386 (1980)

    MathSciNet  Google Scholar 

  52. R. Dashen, S. Ma, H.J. Bernstein: Phys. Rev. 187, 345 (1969)

    Article  MATH  ADS  Google Scholar 

  53. Y. Avishai, Y.B. Band: Phys. Rev. B 32, 2674 (1985)

    Article  ADS  Google Scholar 

  54. W. Trzeciakowski, M. Gurioli: J. Phys. Condensed Matter 5, 105 (1993); 5, 1701 (1993)

    Article  ADS  Google Scholar 

  55. H.W. Jang, S.E. Choi, J.C. Light: J. Chem. Phys. 100, 4188 (1994)

    Article  ADS  Google Scholar 

  56. V. Gasparian, M. Pollak: Phys. Rev. B 47, 2038 (1993)

    Article  ADS  Google Scholar 

  57. G. Iannaccone: Phys. Rev. 51 51, 4727 (1995)

    Article  Google Scholar 

  58. G. Iannaccone, B. Pellegrini: Phys. Rev. B 53, 2020 (1996)

    Article  ADS  Google Scholar 

  59. E.P. Wigner: Phys. Rev. 98, 145 (1955)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. W. van Dijk, K.A. Kiers: Am. J. Phys. 60, 520 (1992)

    Article  ADS  Google Scholar 

  61. J.G. Muga, J.P. Palao: Ann. Phys. 7, 671 (1998).

    Article  Google Scholar 

  62. H.M. Nussenzveig: Causality and Dispersion Relations (Academic Press, New York (1972)

    Google Scholar 

  63. A. Galindo, P. Pascual: Quantum Mechanics I,II (Springer-Verlag, Berlin 1990,(1991)

    Google Scholar 

  64. Ph.A. Martin: Acta Phys. Austriaca Suppl. 23, 159 (1981)

    Google Scholar 

  65. M. Sassoli de Bianchi: J. Math. Phys. 35, 2719 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  66. V.F. Weiskopf, B.P. Wigner: Z. Phys. 63, 54 (1930); 65, 18 (1930)

    Article  ADS  Google Scholar 

  67. H. Jakobovits, Y. Rothschild, J. Lecitan: Am. J. Phys. 63, 439 (1995)

    Article  ADS  Google Scholar 

  68. G. García Calderón, J.L. Mateos, M. Moshinsky: Phys. Rev. Lett. 74, 337 (1995)

    Article  ADS  Google Scholar 

  69. J.G. Muga, G.W. Wei, R.F. Snider: Ann. Phys. 252, 336 (1996)

    Article  ADS  Google Scholar 

  70. J.G. Muga, R.F. Snider, G.W. Wei: Europhysics Letters 35, 247 (1996)

    Article  ADS  Google Scholar 

  71. M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions (Dover, New York (1972); The function w is a particular case of Moshinsky’s function, see [73] and H. M. Nussenzveig: in Symmetries in Physics, ed. by A. Frank, K. B. Wolf (Springer, Berlin, Heidelberg 1992) pp. 293

    MATH  Google Scholar 

  72. B. Misra, E.C.G. Sudarshan: J. Math. Phys. 18, 756 (1977); A. Peres: Am. J. Phys. 48, 931 (1980); W.M.Itano, J.D. Heinzen, J.J. Bollinger, D.J. Winely: Phys. Rev. A 41, 2295 (1990); K. Urbanowski: Phys. Rev. A 50, 2847 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  73. M. Moshinsky: Phys. Rev. 84, 525 (1951)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  74. G. García Calderón, G. Loyola, M. Moshinsky: in Symmetries in Physics, ed. by A. Frank and K. B. Wolf (Springer, Berlin, Heidelberg (1992) pp. 273.

    Google Scholar 

  75. J.G. Muga, V. Delgado, R.F. Snider: Phys. Rev. B 52, 16381 (1995)

    Article  ADS  Google Scholar 

  76. K. Unnikrishnan: Am. J. Phys. 66, 632 (1998)

    Article  ADS  Google Scholar 

  77. K.W.H. Stevens: Eur. J. Phys. 1, 98 (1989)

    Article  MathSciNet  Google Scholar 

  78. K.W.H. Stevens: J. Phys. C: Solid State Phys. 16, 3649 (1983)

    Article  ADS  Google Scholar 

  79. L. Brillouin: Wave propagation and Group Velocity (Academic Press, New York 1960)

    MATH  Google Scholar 

  80. S. Brouard, J.G. Muga: Phys. Rev. A 54, 3055 (1996)

    Article  ADS  Google Scholar 

  81. J.G. Muga, J.P. Palao: J. Phys. A 31, 9519 (1998)

    Article  ADS  Google Scholar 

  82. J.G. Muga, M. Büttiker: Phys. Rev. A 62, 023808 (2000)

    Article  ADS  Google Scholar 

  83. P. Moretti: Phys. Scr. 45, 18 (1992)

    Article  ADS  Google Scholar 

  84. M. Büttiker, R. Landauer: Phys. Rev. Lett. 49, 1739 (1982)

    Article  ADS  Google Scholar 

  85. A. Ranfagni, D. Mugnai, P. Fabeni, P. Pazzi: Physica Scripta 42, 508 (1990)

    Article  ADS  Google Scholar 

  86. A. Ranfagni, D. Mugnai, A. Agresti: Phys. Lett. A 158, 161 (1991)

    Article  ADS  Google Scholar 

  87. N. Teranishi, A.M. Kriman, D.K. Ferry: Superlattices and Microstructures 3, 509 (1987)

    Article  ADS  Google Scholar 

  88. A.P. Jauho, M. Jonson: Superlattices and Microstructures 6, 303 (1989)

    Article  ADS  Google Scholar 

  89. M. Büttiker, H. Thomas: Ann. Phys. (Leipzig) 7, 602 (1998); Superlattices and Microstructures 23 781 (1998)

    Article  ADS  Google Scholar 

  90. A.D. Baute, I.L. Egusquiza, J.G. Muga: J. Phys. A 34, 4289 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  91. H.M. Nussenzveig: in Symmetries in Physics. ed. by A. Frank, Wolf (Springer, Berlin, Heidelberg 1992) pp.293

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Química-Física, Universidad del País Vasco, Apdo 644, Bilbao, Spain

    J. Gonzalo Muga

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  1. J. Gonzalo Muga
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Editors and Affiliations

  1. Departamento de Química-Física Facultad de Ciencias, Universidad del País Vasco, Apdo. 644, Bilbao, Spain

    J. G. Muga

  2. Departamento de Física Fundamental II, Universidad de La Laguna, La Laguna (S/C de Tenerife), Spain

    R. Sala Mayato

  3. Fisika Teorikoaren Saila Zientzi Fakultatea, Euskal Herriko Unibertsitatea, 644 P.K., Bilbao, Spain

    I. L. Egusquiza

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Gonzalo Muga, J. (2002). Characteristic Times in One-Dimensional Scattering. In: Muga, J.G., Mayato, R.S., Egusquiza, I.L. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45846-8_2

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  • DOI: https://doi.org/10.1007/3-540-45846-8_2

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