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2011 | 9 | 1 | 1-12
Article title

The Maslov correction in the semiclassical Feynman integral

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EN
Abstracts
EN
The Maslov correction to the wave function is the jump of $$
\left( { - \frac{\pi }
{2}} \right)
$$ in the phase when the system passes through a caustic. This can be explained by studying the second variation and the geometry of paths, as conveniently seen in Feynman’s path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.
Publisher
Journal
Year
Volume
9
Issue
1
Pages
1-12
Physical description
Dates
published
1 - 2 - 2011
online
24 - 9 - 2010
References
  • [1] M. Gouy, Comptes rendus hebdomadaires des séances de l’Académie des Sciences 110, 1251 (1890)
  • [2] J.B. Keller, Ann. Phys. 4, 180 (1958) http://dx.doi.org/10.1016/0003-4916(58)90032-0[Crossref]
  • [3] V.P. Maslov, Asymptotic methods in the calculus of perturbations (MGU, Moscow, 1965) (in Russian)
  • [4] V.I. Arnold, Funktional’nyi Analiz i Ego Prilozheniya 1, 1 (1967) (in Russian) http://dx.doi.org/10.1007/BF01075861[Crossref]
  • [5] J.-M. Souriau, Lec. Notes Phys. 50, 117 (1976) http://dx.doi.org/10.1007/3-540-07789-8_13[Crossref]
  • [6] V. Marino, L. Gualandari, Indice di Maslov. Lezioni del Prof. Souriau, Pubblicazioni del’Istituto di Matematica Applicata N. 191. Università di Roma (1977) (in Italian)
  • [7] R.P. Feynman, A.R. Hibbs, Quantum Mechanics and path integrals (McGraw-Hill, New York, 1965)
  • [8] P.A. Horváthy, Int. J. Theor. Phys. 18, 245 (1979) http://dx.doi.org/10.1007/BF00671761[Crossref]
  • [9] L.S. Schulman, In: A.M. Arthurs (Ed.),, Functional integration and its applications (Clarendon Pross, Oxford, 1975) 144
  • [10] B.K. Cheng, Int. J. Theor. Phys. 23, 1099 (1984) http://dx.doi.org/10.1007/BF02213422[Crossref]
  • [11] J.Q. Liang, G. Morandi, Phys. Lett. A 160, 9 (1991) http://dx.doi.org/10.1016/0375-9601(91)90197-G[Crossref]
  • [12] P.A. Horváthy, L. Úry, Acta Phys. Hung. 42, 251 (1977) http://dx.doi.org/10.1007/BF03157493[Crossref]
  • [13] P.A. Horváthy, Phys. Lett. A 76, 11 (1980) http://dx.doi.org/10.1016/0375-9601(80)90133-4[Crossref]
  • [14] P.A. Horváthy, Lect. Notes Math. 836, 67 (1980) http://dx.doi.org/10.1007/BFb0089727[Crossref]
  • [15] B.K. Cheng, Phys. Scripta 29, 351 (1984) http://dx.doi.org/10.1088/0031-8949/29/4/012[Crossref]
  • [16] B.K. Cheng, Phys. Rev. A 30, 1491 (1984) http://dx.doi.org/10.1103/PhysRevA.30.1491[Crossref]
  • [17] G. Sagnac, Comptes rendus hebdomadaires des séances de l’Académie des Sciences 157, 708 (1913)
  • [18] F. Hasselbach, M. Niklas, Phys. Rev. A 48, 143 (1993) http://dx.doi.org/10.1103/PhysRevA.48.143[Crossref]
  • [19] R. Anderson, H.R. Bilger, G.E. Stedman, Am. J. Phys. 62, 975 (1994) http://dx.doi.org/10.1119/1.17656[Crossref]
  • [20] F. Hasselbach, Rep. Prog. Phys. 73, 016101 (2010) http://dx.doi.org/10.1088/0034-4885/73/1/016101[Crossref]
  • [21] C. DeWitt-Morette, Ann. Phys. 97, 367 (1976) http://dx.doi.org/10.1016/0003-4916(76)90041-5[Crossref]
  • [22] S. Levit, U. Smilansky, Ann. Phys. 103, 198 (1977) http://dx.doi.org/10.1016/0003-4916(77)90269-X[Crossref]
  • [23] M. Morse, Calculus of variations in the large (Transactions of the AMS, Providence, 1934)
  • [24] J. Milnor, Morse Theory (Princeton U.P., Princeton, 1963)
  • [25] W.H. Miller, J. Chem. Phys. 53, 1949 (1970) http://dx.doi.org/10.1063/1.1674275[Crossref]
  • [26] W.H. Miller, Adv. Chem. Phys. 25, 69 (1974) http://dx.doi.org/10.1002/9780470143773.ch2[Crossref]
  • [27] R.A. Marcus, J. Chem. Phys. 54, 3965 (1971) http://dx.doi.org/10.1063/1.1675453[Crossref]
  • [28] S. Levit, U. Smilansky, D. Pelte, Phys. Lett. B 53, 39 (1974) http://dx.doi.org/10.1016/0370-2693(74)90338-4[Crossref]
  • [29] H. Massman, J.O. Rasmussen, Nucl. Phys. A 243, 155 (1975) http://dx.doi.org/10.1016/0375-9474(75)90026-3[Crossref]
  • [30] T. Koeling, R.A. Malfliet, Phys. Rep. C 22, 181 (1975) http://dx.doi.org/10.1016/0370-1573(75)90059-9[Crossref]
  • [31] K. Horie, H. Miyazaki, I. Tsutsui, Ann. Phys. 273, 267 (1999) http://dx.doi.org/10.1006/aphy.1999.5905[Crossref]
  • [32] K. Horie, H. Miyazaki, I. Tsutsui, Ann. Phys. 279, 104 (2000) http://dx.doi.org/10.1006/aphy.1999.5971[Crossref]
  • [33] C-I Um, K-H Yeon, J. Korean Phys. Soc. 41, 594 (2002)
  • [34] C-I Um, K-H Yeon, T.F. George, Phys. Rep. 362, 63 (2002) http://dx.doi.org/10.1016/S0370-1573(01)00077-1[Crossref]
  • [35] H. Kleinert, Path integrals in Quantum Mechanics, 4th Edition (World Scientific, Singapore, 2004)
  • [36] C. Grosche, F. Steiner, Springer Tr. Mod. Phys. 145, 1 (1998) http://dx.doi.org/10.1007/BFb0109521[Crossref]
  • [37] P.Y. Cai, A. Inomata, P. Wang, Phys. Lett. A 91, 331 (1982) http://dx.doi.org/10.1016/0375-9601(82)90425-X[Crossref]
  • [38] G. Junker, A. Inomata, Phys. Lett. A 110, 195 (1985) http://dx.doi.org/10.1016/0375-9601(85)90122-7[Crossref]
  • [39] J.M. Cai, P.Y. Cai, A. Inomata, In: J.Q. Liang, M.L. Wang, S.N. Qiao, D.C. Su (Eds.), ISATQP-Shanxi, 1992, Shanxi, China (Science Press, Beijing, 1993)
  • [40] U. Niederer, Helv. Phys. Acta 46, 192 (1973)
  • [41] C. Duval, G. Gibbons, A. Horváthy, Phys. Rev. D 43, 3907 (1991) http://dx.doi.org/10.1103/PhysRevD.43.3907[Crossref]
  • [42] C. Duval, P.A. Horváthy, L. Palla, Phys. Rev. D 50, 6658 (1994) http://dx.doi.org/10.1103/PhysRevD.50.6658[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-010-0055-3
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