Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina


IMPACT FACTOR 2017: 0.755
5-year IMPACT FACTOR: 0.820

CiteScore 2017: 0.83

SCImago Journal Rank (SJR) 2017: 0.241
Source Normalized Impact per Paper (SNIP) 2017: 0.537

ICV 2017: 162.45

Open Access
Online
ISSN
2391-5471
See all formats and pricing
More options …
Volume 10, Issue 2

Issues

Volume 13 (2015)

Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition

Massimiliano Sassoli de Bianchi
Published Online: 2012-03-31 | DOI: https://doi.org/10.2478/s11534-011-0105-5

Abstract

We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”

Keywords: time-delay; sojourn time; scattering theory; time-dependent potentials; non-spatiality

  • [1] E. P. Wigner, Phys. Rev. 98, 145 (1955) http://dx.doi.org/10.1103/PhysRev.98.145CrossrefGoogle Scholar

  • [2] L. Eisenbud, PhD. thesis, Princeton University (Princeton, United States, 1948) Google Scholar

  • [3] F. T. Smith, Phys. Rev. 118, 349 (1960) http://dx.doi.org/10.1103/PhysRev.118.349CrossrefGoogle Scholar

  • [4] M. Goldberger, K. M. Watson, Collision theory (John Wiley Sons, New York, 1964) Google Scholar

  • [5] J. M. Jauch, J.-P. Marchand, Helv. Phys. Acta 40, 217 (1967) Google Scholar

  • [6] J. M. Jauch, K. B. Sinha, B. N. Misra, Helv. Phys. Acta 45, 398 (1972) Google Scholar

  • [7] D. Bollé, T. A. Osborn, Phys. Rev. D 11, 3417 (1975) http://dx.doi.org/10.1103/PhysRevD.11.3417CrossrefGoogle Scholar

  • [8] P. A. Martin, Acta Phys. Austriaca, Suppl. 23, 157 (1981) Google Scholar

  • [9] W. O. Amrein, M. B. Cibils, Helv. Phys. Acta 60, 481 (1987) Google Scholar

  • [10] W. O. Amrein, M. B. Cibils, K. B. Sinha, Annales de l’Institut Henri Poincaré 47, 367 (1987) Google Scholar

  • [11] M. Sassoli de Bianchi, Ph. A. Martin, Helv. Phys. Acta 65, 1119 (1992) Google Scholar

  • [12] C. Gérard, R. Tiedra de Aldecoa, J. Math. Phys. 48, 122101 (2007) http://dx.doi.org/10.1063/1.2816255CrossrefGoogle Scholar

  • [13] S. Richard, R. Tiedra de Aldecoa, arXiv:1008.3433 [math-ph] Google Scholar

  • [14] H. Salecker, E. P. Wigner, Phys. Rev. 109, 217 (1958) http://dx.doi.org/10.1103/PhysRev.109.571CrossrefGoogle Scholar

  • [15] A. I. Baz’, Sov. J. Nucl. Phys.+ 4, 182 (1967) Google Scholar

  • [16] V. F. Rybachenko, Sov. J. Nucl. Phys.+ 5, 635 (1967) Google Scholar

  • [17] T. E. Hartman, Tunneling of a wave packet, J. Appl. Phys. 33, 3427 (1962) http://dx.doi.org/10.1063/1.1702424CrossrefGoogle Scholar

  • [18] E. H. Hauge, J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989) http://dx.doi.org/10.1103/RevModPhys.61.917CrossrefGoogle Scholar

  • [19] V. S. Olkhovsky, E. Recami, Phys. Rep. 214, 339 (1992) http://dx.doi.org/10.1016/0370-1573(92)90015-RCrossrefGoogle Scholar

  • [20] V. S. Olkhovsky, E. Recami, Advances in Mathematical Physics, DOI:10.1155/2009/859710. CrossrefGoogle Scholar

  • [21] V. S. Olkhovsky, E. Recami, J. Jakielc, Phys. Rep. 398, 133 (2004) http://dx.doi.org/10.1016/j.physrep.2004.06.001CrossrefGoogle Scholar

  • [22] E. Recami, V. S. Olkhovsky, S. P. Maydanyuk, Int. J. Mod. Phys. A, 25, 9, 1785 (2010) http://dx.doi.org/10.1142/S0217751X10048007CrossrefGoogle Scholar

  • [23] V. S. Olkhovsky, Phys. Usp.+ 54, 829 (2011) http://dx.doi.org/10.3367/UFNe.0181.201108d.0859CrossrefGoogle Scholar

  • [24] R. Landauer, Th. Martin, Rev. Mod. Phys. 66, 217 (1992) http://dx.doi.org/10.1103/RevModPhys.66.217CrossrefGoogle Scholar

  • [25] J. Muga et al. (Eds.), Lect. Notes Phys. 1, 734 (2008) Google Scholar

  • [26] J. Muga et al. (Eds.), Lect. Notes Phys. 2, 789 (2009) Google Scholar

  • [27] W. Jaworski, D. Wardlaw, Phys. Rev. A 37, 2843 (1988) http://dx.doi.org/10.1103/PhysRevA.37.2843CrossrefGoogle Scholar

  • [28] W. Jaworski, D. Wardlaw, Phys. Rev. A 38, 5404 (1988) http://dx.doi.org/10.1103/PhysRevA.38.5404CrossrefGoogle Scholar

  • [29] W. Jaworski, D. Wardlaw, Phys. Rev. A 40, 6210 (1989) http://dx.doi.org/10.1103/PhysRevA.40.6210CrossrefGoogle Scholar

  • [30] W. Jaworski, D. Wardlaw, Phys. Rev. A 43, 5137 (1991) http://dx.doi.org/10.1103/PhysRevA.43.5137CrossrefGoogle Scholar

  • [31] M. Sassoli de Bianchi, Helv. Phys. Acta 66, 361 (1993) Google Scholar

  • [32] P. A. Martin, M. Sassoli de Bianchi, J. Phys. A-Math. Gen. 25, 3627 (1992) http://dx.doi.org/10.1088/0305-4470/25/12/023CrossrefGoogle Scholar

  • [33] H. Narnhofer, Phys. Rev. D 22, 2387 (1980) http://dx.doi.org/10.1103/PhysRevD.22.2387CrossrefGoogle Scholar

  • [34] G. Temple, Nature 135, 957 (1935) http://dx.doi.org/10.1038/135957a0CrossrefGoogle Scholar

  • [35] J. Hilgevoord, Am. J. Phys. 70, 301 (2002) http://dx.doi.org/10.1119/1.1430697CrossrefGoogle Scholar

  • [36] G. R. Allcock, Ann. Phys. New York 53, 253 (1969) http://dx.doi.org/10.1016/0003-4916(69)90251-6CrossrefGoogle Scholar

  • [37] R. Werner, J. Math. Phys. 27, 793 (1986) http://dx.doi.org/10.1063/1.527184CrossrefGoogle Scholar

  • [38] K. Kong Wan, R. H. Fountain, Z. Y. Tao, J. Phys. AMath. Gen. 28, 2379 (1995) http://dx.doi.org/10.1088/0305-4470/28/8/028CrossrefGoogle Scholar

  • [39] J.G. Muga, C.R. Leavens, Phys. Rep. 338, 353 (2000) http://dx.doi.org/10.1016/S0370-1573(00)00047-8CrossrefGoogle Scholar

  • [40] W. O. Amrein, J. M. Jauch, K. B. Sinha, Scattering theory in quantum mechanics (Benjamin, Reading, 1977) Google Scholar

  • [41] A. Jensen, Commun. Math. Phys. 82, 435 (1981) http://dx.doi.org/10.1007/BF01237049CrossrefGoogle Scholar

  • [42] P. A. Martin, M. Sassoli de Bianchi, Found. Phys. 24, 1371 (1994) http://dx.doi.org/10.1007/BF02283038CrossrefGoogle Scholar

  • [43] W. Jaworski, D. Wardlaw, Phys. Rev. A 45, 292 (1992) http://dx.doi.org/10.1103/PhysRevA.45.292CrossrefGoogle Scholar

  • [44] R. Golub et al., Phys. Lett. A 148, 27 (1990) http://dx.doi.org/10.1016/0375-9601(90)90568-9CrossrefGoogle Scholar

  • [45] P. A. Martin, Nuovo Cimento 30B, 217 (1975) Google Scholar

  • [46] W. Jaworski, J. Math. Phys. 30, 1505 (1989) http://dx.doi.org/10.1063/1.528282CrossrefGoogle Scholar

  • [47] R. Lavine, J. Funct. Anal. 12, 30 (1973) http://dx.doi.org/10.1016/0022-1236(73)90088-8CrossrefGoogle Scholar

  • [48] J. A. Damborenea, I. L. Egusquiza, J. G. Muga, Am. J. Phys. 70, 738 (2002) http://dx.doi.org/10.1119/1.1473643CrossrefGoogle Scholar

  • [49] J. E. G. Farina, Am. J. Phys. 61, 466 (1992) http://dx.doi.org/10.1119/1.17243CrossrefGoogle Scholar

  • [50] P. A. Martin, Commun. Math. Phys. 47, 221 (1976) http://dx.doi.org/10.1007/BF01609841CrossrefGoogle Scholar

  • [51] D. Bollé, J. D’Hondt, J. Phys. A-Math. Gen. 14, 1663 (1981) http://dx.doi.org/10.1088/0305-4470/14/7/022CrossrefGoogle Scholar

  • [52] H. Narnhofer, W. Thirring, Phys. Rev. A 23, 1688 (1981) http://dx.doi.org/10.1103/PhysRevA.23.1688CrossrefGoogle Scholar

  • [53] V. S. Olkhovsky, Sov. J. Nucl. Phys. 15, 130 (1984) Google Scholar

  • [54] V. S. Olkhovsky, Nukleonika 35, 99 (1990) Google Scholar

  • [55] R. Bonifaccio (Ed.), AIP, 272 (1998) Google Scholar

  • [56] V. S. Olkhovsky, E. Recami, A. I. Gerasimchuk, Nuovo Cimento 22A, 263 (1974) Google Scholar

  • [57] B. J. Verhaar et al., Physica 91A, 119 (1978) Google Scholar

  • [58] J. P. Falck, E. H. Hauge, Phys. Rev. B 38, 3287 (1988) http://dx.doi.org/10.1103/PhysRevB.38.3287CrossrefGoogle Scholar

  • [59] D. S. Saraga, M. Sassoli de Bianchi, Helv. Phys. Acta 70, 751 (1997) Google Scholar

  • [60] D. R. Yafaev, In: A. Boutet de Monvel et al. (Ed.), Recent developments in quantum mechanics (Kluwer Academic Publishers, Netherlands, 1991) 367 http://dx.doi.org/10.1007/978-94-011-3282-4_21CrossrefGoogle Scholar

  • [61] P. A. Martin, M. Sassoli de Bianchi, J. Phys. A-Math. Gen. 28, 2403 (1995) http://dx.doi.org/10.1088/0305-4470/28/8/030CrossrefGoogle Scholar

  • [62] D. Aerts, In: D. Aerts, J. Broekaert, E. Mathijs (Eds.), The white book of ”Einstein meets Magritte” (Kluwer Academic Publishers, Dordrecht, 1999) 129 Google Scholar

  • [63] D. Aerts, In: Elena Castellani (Ed.), Interpreting bodies, classical and quantum objects in modern physics (Princeton University Press, Princeton, 1998) 223 Google Scholar

  • [64] M. Sassoli de Bianchi, Found. Sci. 16, 393 (2011) http://dx.doi.org/10.1007/s10699-011-9227-xCrossrefGoogle Scholar

  • [65] M. Büttiker, Phys. Rev. B 27, 6178 (1983) http://dx.doi.org/10.1103/PhysRevB.27.6178CrossrefGoogle Scholar

  • [66] D. Bollé, T. A. Osborn, J. Math. Phys. 20, 1121 (1979) http://dx.doi.org/10.1063/1.524164CrossrefGoogle Scholar

  • [67] W. O. Amrein, P. Jacquet, Phys. Rev. A 75, 022106 (2007) http://dx.doi.org/10.1103/PhysRevA.75.022106CrossrefGoogle Scholar

  • [68] R. Tiedra de Aldecoa, Annales de l’Institut Henri Poincaré 7, 105 (2006) http://dx.doi.org/10.1007/s00023-005-0243-7CrossrefGoogle Scholar

  • [69] M. Sassoli de Bianchi, J. Math. Phys. 35, 2719 (1994) http://dx.doi.org/10.1063/1.530481CrossrefGoogle Scholar

  • [70] M. Sassoli de Bianchi, Found. Sci., DOI: 10.1007/s10699-011-9233-z (in press) CrossrefGoogle Scholar

About the article

Published Online: 2012-03-31

Published in Print: 2012-04-01


Citation Information: Open Physics, Volume 10, Issue 2, Pages 282–319, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-011-0105-5.

Export Citation

© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Renate Pazourek, Stefan Nagele, and Joachim Burgdörfer
Reviews of Modern Physics, 2015, Volume 87, Number 3, Page 765
[2]
V V Dodonov and A V Dodonov
Physica Scripta, 2015, Volume 90, Number 7, Page 074049
[4]
Massimiliano Sassoli de Bianchi
Foundations of Science, 2013, Volume 18, Number 1, Page 11
[5]
A Gournay and R Tiedra de Aldecoa
Journal of Physics A: Mathematical and Theoretical, 2012, Volume 45, Number 21, Page 215204

Comments (0)

Please log in or register to comment.
Log in