Quantum wave packet revivals

Physics Reports

Volumn 392, Issue 1-2, 2004, Pages 1-119

  Robinett, Rick W ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Collapse; Dynamics; Fractional revival; Long term evolution; Quantum; Revival; Spectrum; Wave packet

Indexed keywords

EID: 0442328987     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2003.11.002     Document Type: Review

References (364)

1. Schrödinger E. Der stetige Übergang von der Mikro- zur Makromechanik Naturwissenschaften 14 1926 664-666, translated and reprinted as The continuous transition from micro- to macro mechanics, Collected paperson wave mechanics, Chelsea Publishing, New York, 1982, pp. 41-44.
2. Kennard E.H. The quantum mechanics of an electron or other particle J. Franklin Institute 207 1929 47-78 see also Zur Quantenmechanikeinfacher Bewegungstypen (translated as The quantum mechanics of simple typesof motion), Z. Phys. 44 (1927) 326-352.
3. Darwin C.G. Free motion in the wave mechanics Proc. R. Soc (London) A 117 1928 258-293
4. de Broglie L. Einführung in die Wellenmechanik 1929 Akad. Verlag Leipzig
5. E.C. Kemble, The Fundamental Principles of Quantum Mechanics with Elementary Applications, McGraw-Hill, New York, 1937, pp. 35-41.
6. S. Dushman, The Elements of Quantum Mechanics, Wiley, New York, 1938, pp. 405-407.
7. V. Rojansky, Introductory Quantum Mechanics, Prentice-Hall, New York, 1938, pp. 66-70.
8. Letter from Lorentz to Schrödinger, 1926, reprinted in: K. Przibram (Eds.), Letters on Wave Mechanics, Philosophical Library, New York, 1967, pp. 67-75.
9. Brown L.S. Classical limit of the hydrogen atom Am. J. Phys. 41 1973 525-530
10. Mostowski J. On the classical limit of the Kepler problem Lett. Math. Phys. 2 1977 1-5
11. Nieto M.M. Simmons Jr. L.M. Coherent states for general potentials Phys. Rev. Lett. 41 1978 207-210
12. Nieto M.M. Coherent states for general potentials IV. Three-dimensional systems Phys. Rev. D 22 1980 391-402
13. Gutschick V.P. Nieto M.M. Coherent states for general potentials V. Time evolution Phys. Rev. D 22 1980 403-418
14. Snider D.R. Elliptical orbits in quantum mechanics Am. J. Phys. 51 1983 801-803
15. Gerry C.C. Coherent states and the Kepler-Coulomb problem Phys. Rev. A 33 1986 6-11
16. Bhaumik D. Dutta-Roy B. Ghosh G. Classical limit of the hydrogen atom J. Phys. A 19 1986 1355-1364
17. Alber G. Ritsch H. Zoller P. Generation and detection of Rydberg wave packets by short laser pulses Phys. Rev. A 34 1986 1058-1064
18. Noordam L.D. Duncan D.I. Gallagher T.F. Ramsey fringes in atomic Rydberg wave packets Phys. Rev. A 45 1992 4734-4737
19. Alber G. Zoller P. Laser excitation of electronic wave packets in Rydberg atoms Phys. Rep. 199 1991 231-280
20. Garraway B.M. Suominen K.-A. Wave-packet dynamics: new physics and chemistry in femto-time Rep. Prog. Phys. 58 1995 365-419
21. J.A. Yeazell, T. Uzer (Eds.), in: The Physics and Chemistry of Wave Packets, Wiley, New York, 2000.
22. Verlet J.R.R. Fielding H.H. Manipulating electron wave packets Int. Rev. Phys. Chem. 20 2001 283-312
23. Smith R.A.L. Verlet J.R.R. Fielding H.H. Rydberg wave packets in molecules Phys. Chem. Chem. Phys. 5 2003 3567-3579
24. Yeazell J.A. Stroud C.R. Jr. Observation of spatially localized atomic electron wave-packets Phys. Rev. Lett. 60 1988 1494-1497
25. Noordam L.D. ten Wolde A. Muller H.G. Lagendijk A. van Linden van den Heuvell H.B. Return of an electronic wavefunction to the core J. Phys. B 21 1988 L533-L538
26. ten Wolde A. Noordam L.D. Lagendijk A. van Linden van den Heuvell H.B. Observation of radially localized atomic electron wave packets Phys. Rev. Lett. 61 1988 2099-2101
27. Yeazell J.A. Mallalieu M. Parker J. Stroud C.R. Jr. Classical periodic motion of atomic-electron wave packets Phys. Rev. A 40 1989 5040-5043
28. Parker J. Stroud Jr. C.R. Coherence and decay of Rydberg wave packets Phys. Rev. Lett. 56 1986 716-719
29. Parker J. Stroud Jr. C.R. Rydberg wave packets and the classical limit Phys. Scr. T 12 1986 70-75
30. Yeazell J.A. Mallalieu M. Stroud Jr. C.R. Observation of the collapse and revival of a Rydberg electronic wave packet Phys. Rev. Lett. 64 1990 2007-2010
31. Yeazell J.A. Stroud Jr. C.R. Observation of fractional revivals in the evolution of a Rydberg atomic wave packet Phys. Rev. A 43 1991 5153-5156
32. Meacher D.R. Meyler P.E. Hughes I.G. Ewart P. Observation of the collapse and revival of a Rydberg wavepacket in atomic rubidium J. Phys. B. 24 1991 L63-L69
33. Wals J. Fielding H.H. Christian J.F. Snoek L.C. van der Zande W.J. van Linden van den Heuvell H.B. Observation of Rydberg wave packet dynamics in a Coulombic and magnetic field Phys. Rev. Lett. 72 1994 3783-3786
34. Averbukh I.Sh. Perelman N.F. Fractional revivals: universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics Phys. Lett. A 139 1989 449-453
35. Averbukh I.Sh. Perelman N.F. Fractional revivals of wave packets Acta Phys. Pol. 78 1990 33-40 This paperincludes much of the material in the citation above, correcting some minor typographical errors
36. Averbukh I.Sh. Perelman N.F. Fractional regenerations of wave-packets in the course of long-term evolution of highly excited quantum-systems Zh. Eksp. Teor. Fiziki. 96 1989 818-827 (Sov. Phys. JETP 69 (1989) 464-469)
37. Vrakking M.J.J. Villeneuve D.M. Stolow A. Observation of fractional revivals of a molecular wave packet Phys. Rev. A 54 1996 R37-R40
38. Nauenberg M. Stroud C. Yeazell J. The classical limit of an atom Sci. Am. 270 1994 44-49
39. Averbukh I.Sh. Perelman N.F. The dynamics of wave packets of highly-excited atoms and molecules Usp. Fiz. Nauk 161 1991 41-81
40. Bluhm R. Kostelecký V.A. Porter J. The evolution and revival structure of localized quantum wave packets Am. J. Phys. 64 1996 944-953 [arXiv:quant-ph/9510029].
41. Mandelstam L. Tamm I. The uncertainty relation between energy and time in nonrelativistic quantum mechanics J. Phys. (USSR) 9 1945 249-254
42. Nauenberg M. Autocorrelation function and quantum recurrence of wave packets J. Phys. B. At. Mol. Opt. Phys. 23 1990 L385-L390
43. Bocchieri P. Loinger A. Quantum recurrence theorem Phys. Rev. 107 1957 337-338
44. von Baltz R. Distance between quantum states and the motion of wave packets Eur. J. Phys. 11 1990 215-220
45. Bohr H. Almost periodic functions 1947 Chelsea New York
46. Percival I.C. Almost periodicity and the quantal H theorem J. Math. Phys. 2 1961 235-239
47. Ermoshin V.A. Erdmann M. Engel V. Fermi-Pasta-Ulam recurrences, normal modes, and wave-packet revivals Chem. Phys. Lett. 356 2002 29-35
48. E. Fermi, J. Pasta, S. Ulam, Document LA-1940 Los Alamos Preprint (May 1995). Reprinted as Studies of non-linear problems, in: E. Segrè (Ed.), Collected papers of Enrico Fermi, Vol. II, University of Chicago, Chicago, 1965, pp. 978-988.
49. Hogg T. Huberman B.A. Recurrence phenomena in quantum dynamics Phys. Rev. Lett. 48 1982 711-714
50. Peres A. Multiple time scales for recurrences of Rydberg states Phys. Rev. A 47 1993 5196-5197
51. Bohr N. Über die Anwendung der Quantentheorie auf den Atombau. I. Die Grundpostulate der Quantentheorie Z. Phys. 13 1923 117-165
52. H. Goldstein, Classical Mechanics, 2nd Edition, Addison-Wesley, Reading, MA, 1980, pp. 457-471.
53. A.L. Fetter, J.D. Walecka, Theoretical mechanics of particles and continua, McGraw-Hill, New York, 1980, pp. 191-196.
54. A.B. Migdal, V. Krainov, Approximation Methods in Quantum Mechanics, Benjamin, New York, 1969, pp. 111-144.
55. Saxon D.W. Elementary Quantum Mechanics 1968 McGraw-Hill New York
56. See, e.g., C. Cohen-Tannoudji, D. Diu, F. Laloë, Quantum Mechanics, Vol. II, Wiley, New York, 1977, pp. 1110-1116.
57. Sukhatme U.P. WKB energy levels for a class of one-dimensional potentials Am. J. Phys. 41 1973 1015-1016
58. Nieto M.M. Simmons Jr. L.M. Limiting spectra from confining potentials Am. J. Phys. 47 1979 634-635
59. 2N and the correspondence principle Int. J. Theor. Phys. 18 1979 185-191
60. Robinett R.W. Wave packet revivals and quasirevivals in one-dimensional power law potentials J. Math. Phys. 41 2000 1801-1813
61. Quigg C. Rosner J.L. Quantum mechanics with applications to quarkonium Phys. Rep. 56 1979 167-235
62. Greiner M. Mandel O. Hänsch T.W. Bloch I. Collapse and revival of the matter wave field of a Bose-Einstein condensate Nature 419 2002 51-54
63. Yurke B. Stoler D. Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion Phys. Rev. Lett. 57 1986 13-16
64. Yurke B. Stoler D. Quantum behavior of a four-wave mixer operated in a nonlinear regime Phys. Rev. A 35 1987 4846-4849
65. Yurke B. Stoler D. The dynamic generation of Schrödinger cats and their detection Physica B 151 1988 298-301
66. Milburn G.J. Quantum and classical Liouville dynamics of the anharmonic oscillator Phys. Rev. A 33 1986 674-685
67. Noel M.W. Stroud Jr. C.R. Young's double-slit interferometry within an atom Phys. Rev. Lett. 75 1995 1252-1255
68. Noel M.W. Stroud Jr. C.R. Excitation of an atomic electron to a coherent superposition of macroscopically distinct states Phys. Rev. Lett. 77 1996 1913-1916
69. Schleich W.P. Quantum Optics in Phase Space 2001 Wiley-VCH Berlin
70. Mack H. Bienert M. Haug F. Freyberger M. Schleich W.P. Wave packets can factorize numbers Phys. Stat. Sol. B 233 2002 408-415
71. H. Mack, M. Bienert, F. Haug, F.S. Straub, M. Freyberger, W.P. Schleich, Wave packet dynamics and factorization of numbers, in: F. de Martini, C. Monroe (Eds.), Experimental Quantum Computation and Information, Proceedings of the International School of Physics "Enrico Fermi", IOS Press, Amsterdam, 2002, pp. 369-384.
72. Berndt B.C. Evans R.J. Williams K.S. Gauss and Jacobi Sums 1998 Wiley New York
73. Gauss C.F. Disquisitiones Arithmeticae 1801 Fleischer Leipzig
74. Gauss C.F. Summatio quarumdam serierum singularium Comment. Soc. Reg. Sci. Gottingensis 1 1811
75. Leichtle C. Averbukh I.Sh. Schleich W.P. Generic structure of multilevel quantum beats Phys. Rev. Lett. 77 1996 3999-4002
76. Leichtle C. Averbukh I.Sh. Schleich W.P. Multilevel quantum beats: an analytical approach Phys. Rev. A 54 1996 5299-5312
77. Vetchinkin S.I. Vetchinkin A.S. Eryomin V.V. Umanskii I.M. Gaussian wavepacket dynamics in an anharmonic system Chem. Phys. Lett. 215 1993 11-16
78. Eryomin V.V. Vetchinkin S.I. Umanskii I.M. Manifestations of wave packet fractional revivals in a Morse-like anharmonic system J. Chem. Phys. 101 1994 10730-10735
79. Vetchinkin S.I. Eryomin V.V. The structure of wavepacket fractional revivals in a Morse-like anharmonic system Chem. Phys. Lett. 222 1994 394-398
80. Dupret K. Delande D. Nonlinear wave-packet dynamics for a generic one-dimensional time-independent system and its application to the hydrogen atom in a weak magnetic field Phys. Rev. A 53 1996 1257-1272
81. Braun P.A. Savichev V.I. The influence of higher-order anharmonic corrections to the energy spectrum on the evolution of quantum wavepackets J. Phys. B 29 1996 L329-L335
82. Leonhardt U. State reconstruction of anharmonic molecular vibrations: Morse-oscillator model Phys. Rev. A 55 1997 3164-3172
83. Jie Q.-L. Wang S.-J. Wei L.-F. Partial revivals of wave packets: an action-angle phase-space description Phys. Rev. A 57 1998 3262-3267
84. Jie Q.-L. Wang S.-J. Equal partial revivals of wavepackets in long time scales J. Phys. A 33 2000 2513-2525
85. de Polavieja G.G. Noncyclic geometric phase shift for quantal revivals Phys. Rev. Lett. 81 1998 1-5
86. Bluhm R. Kostelecký V.A. Long-term evolution and revival structure of Rydberg wave packets for hydrogen and alkali-metal atoms Phys. Rev. A 51 1995 4767-4786 [arXiv:quant-ph/9506009]
87. Bluhm R. Kostelecký V.A. Long-term evolution and revival structure of Rydberg wave packets Phys. Lett. A 200 1995 308-313 [arXiv:quant-ph/9508024]
88. Knospe O. Schmidt R. Revivals of wave packets: general theory and application to Rydberg clusters Phys. Rev. A 54 1996 1154-1160
89. Bluhm R. Kostelecký V.A. Tudose B. Wave-packet revivals for quantum systems with nondegenerate energies Phys. Lett. A 222 1996 220-226 [arXiv:quant-ph/9609020].
90. Agarwal G.S. Banerji J. Fractional revivals in systems with two time scales Phys. Rev. A 57 1998 3880-3884
91. Gutzwiller M. Chaos in Classical and Quantum Mechanics 1990 Springer New York
92. Gutzwiller M. The Interplay between Classical and Quantum Mechanics 2001 American Association of Physics Teachers College Park, MD
93. Brack M. Bhaduri R.K. Semiclassical Physics 1997 Addison-Wesley Reading, MA
94. Grant A.K. Rosner J.L. Classical orbits in power-law potentials Am. J. Phys. 62 1994 310-315
95. H.A. Bethe, E.E. Salpeter, Quantum Mechanics of One- and Two-electron Atoms, Springer, Berlin, 1957,pp. 27-29, 228-232
96. L.D. Landau, E.M. Lifschitz, Quantum Mechanics: Non-relativistic Theory, 2nd Edition, Pergamon Press, Oxford, 1965, pp. 125-128, 269-274.
97. Holstein B.R. The harmonic oscillator propagator Am. J. Phys. 66 1998 583-589
98. Styer D.F. The motion of wave packets through their expectation values and uncertainties Am. J. Phys. 58 1990 742-744
99. Glauber R.J. Photon correlations Phys. Rev. Lett. 10 1963 84-86
100. Glauber R.J. The quantum theory of optical coherence Phys. Rev. 130 1963 2529-2539
101. Glauber R.J. Coherent and incoherent states of the radiation field Phys. Rev. 131 1963 2766-2788
102. Sudarshan E.C.G. Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams Phys. Rev. Lett. 10 1963 277-279
103. Wright E.M. Walls D.F. Garrison J.C. Collapses and revivals of Bose-Einstein condensates formed in small atomic samples Phys. Rev. Lett. 77 1996 2158-2161
104. Razi Naqvi K. Waldenstrøm S. Revival, mirror revival, and collapse may occur even in a harmonic oscillator wave packet Phys. Scr. 62 2000 12-16 See also S. WaldenstrHm, K. Razi Naqvi, A neglected aspect of thepulsating Gaussian wave packet, Eur. J. Phys. 20 (1999) L41-L43.
105. Segre C.U. Sullivan J.D. Bound-state wave packets Am. J. Phys. 44 1976 729-732 This paper contains oneof the first references to what have become known as wave packet revivals.
106. Aronstein D.L. Stroud Jr. C.R. Fractional wave-function revivals in the infinite square well Phys. Rev. A 55 1997 4526-4537
107. P. Stifter, W.E. Lamb Jr., W.P. Schleich, The particle in a box revisited, in: S.Y. Zhu, M.S. Zubairy, M.O. Scully (Eds.), Frontiers of Quantum Optics and Laser Physics, Proceedings of the International Conference on Quantum Optics and Laser Physics, Springer, Singapore, 1997, pp. 236-246. See also Ref. [93].
108. Lamb Jr. W.E. Suppose Newton had invented wave mechanics Am. J. Phys. 62 1994 201-206
109. Robinett R.W. Visualizing the collapse and revival of wave packets in the infinite square well using expectation values Am. J. Phys. 68 2000 410-420 [arXiv:quant-ph/0307041].
110. Styer D.F. Quantum revivals versus classical periodicity in the infinite square well Am. J. Phys. 69 2001 56-62
111. Razi Naqvi K. Waldenstrøm S. Haji Hassan T. Fractional revival of wave packets in an infinite square well: a Fourier perspective Eur. J. Phys. 22 2001 395-402
112. Doncheski M.A. Heppelmann S. Robinett R.W. Tussey D.C. Wave packet construction in two-dimensional quantum billiards: blueprints for the square, equilateral triangle, and circular cases Am. J. Phys. 71 2003 541-557 [arXiv:quant-ph/0307070].
113. Gori F. Ambrosini D. Borghi R. Mussi V. Santarsiero M. The propagator for a particle in a well Eur. J. Phys. 22 2001 53-66
114. Fulling S.A. Güntürk K.S. Exploring the propagator of a particle in a box Am. J. Phys. 71 2003 55-63
115. Waldenstrøm S. Naqvi K.R. Mork K.J. The force exerted by the walls of an infinite square well on a wave packet: Ehrenfest theorem, revivals and fractional revivals Phys. Scr. 68 2003 45-53
116. Born M. Continuity, determinism, and reality Kgl. Danske Videns. Sels. Mat.-fys. Medd. 30 2 1955 1-26 Born was addressing concerns made by Einstein, in: Elementare K Uberlegungen zur Interpretation derGrundlagen der Quanten-Mechanik, in Scienti,c papers presented to Max Born, Oliver and Boyd, Edinburgh, 1953, pp. 33-40
117. Born M. Ludwig W. Zur Quantenmechanik der kräftefreien Teilchens Z. Phys. 150 1958 106-117
118. Stifter P. Leichtle C. Schleich W.P. Marklov J. Das Teilchen im Kasten: Strukturen in der Wahrscheinlichkeitsdichte (translated as The particle in a box: Structures in the probability density) Z. Naturforsch. 52 A 1997 377-385
119. Kleber M. Exact solutions for time-dependent phenomena in quantum mechanics Phys. Rep. 236 1994 331-393
120. Braun P.A. Savichev V.I. Time dependence of physical observables in wave-packet states Phys. Rev. A 49 1994 1704-1708
121. Doncheski M.A. Robinett R.W. Anatomy of a quantum 'bounce' Eur. J. Phys. 20 1999 29-37 [arXiv:quant-ph/0307010]
122. Wigner E. On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 1932 749-759
123. M. Belloni, M. Doncheski, R.W. Robinett, Wigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets, submitted for publication [arXiv:quant-ph/0312086].
124. Tatarskii V.I. The Wigner representation of quantum mechanics Usp. Fiz. Nauk 139 1983 587-619 (Sov. Phys.Usp. 26 (1983) 311-327).
125. Balaczs N.L. Jennings B.K. Wigner's function and other distribution functions in mock phase space Phys. Rep. 105 1984 347-391
126. Carruthers P. Zachariasen F. Quantum collision theory with phase-space distributions Rev. Mod. Phys. 55 1983 245-285
127. Hillery M. O'Connell R.F. Scully M.O. Wigner E.P. Distribution functions in physics: fundamentals Phys. Rep. 106 1984 121-167
128. Kim Y.S. Wigner E.P. Canonical transformations in quantum mechanics Am. J. Phys. 58 1990 439-448
129. Kim Y.W. Noz M.E. Phase space picture of quantum mechanics: group theoretical approach, in: Lecture Notes in Physics Series Vol. 40 1990 World Scientific Singapore
130. Casas M. Krivine H. Martorell J. On the Wigner transforms of some simple systems and their semiclassical interpretations Eur. J. Phys. 12 1991 105-111
131. Lee H.-W. Theory and application of the quantum phase-space distribution functions Phys. Rep. 259 1995 147-211
132. Ozorio de Almeida A.M. The Weyl representation in classical and quantum mechanics Phys. Rep. 295 1998 265-342
133. Hudson R.L. When is the Wigner quasi-probability density non-negative? Rep. Math. Phys. 6 1974 249-252
134. Sofo F. Claverie P. When is the Wigner function of multi-dimensional systems nonnegative? J. Math. Phys. 24 1983 97-100
135. Ballentine L.E. Quantum Mechanics: A Modern Development 1998 World Scientific Singapore
136. Kinzel W. Bilder elementarer Quantenmechanik Phys. Bl. 51 1995 1190-1191
137. Berry M.V. Quantum fractals in boxes J. Phys. A 29 1996 6617-6629
138. Großmann F. Rost J.-M. Schleich W.P. Spacetime structures in simple quantum systems J. Phys. A 30 1997 L277-L283
139. Marzoli I. Saif F. Bialynicki-Birula I. Friesch O.M. Kaplan A.E. Schleich W.P. Quantum carpets made simple Acta Phys. Slov. 48 1998 323-333 [arXiv:quant-ph/9806033]
140. Kaplan A.E. Stifter P. van Leeuwen K.A.H. Lamb Jr. W.E. Schleich W.P. Intermode traces - fundamental interference phenomena in quantum and wave physics Phys. Scr. T 76 1998 93-97
141. Loinaz W. Newman T.J. Quantum revivals and carpets in some exactly solvable systems J. Phys. A 32 1999 8889-8895 [arXiv:quant-ph/9902039]
142. Hall M.J.W. Reineker M.S. Schleich W.P. Unravelling quantum carpets: a travelling wave approach J. Phys. A 32 1999 8275-8291 [arXiv:quant-ph/9906107]
143. A.E. Kaplan, I. Marzoli, W.E. Lamb Jr., W.P. Schleich, Multimode interference: highly regular pattern formation in quantum wave-packet evolution, Phys. Rev. A 61 (2000) 032101-1-6.
144. Friesch O.M. Marzoli I. Schleich W.P. Quantum carpets woven by Wigner functions New. J. Phys. 2 2000 4.1-4.11 http:/www.jnp.org
145. N quadratic spectra: base-N quantum computer registers,Phys. Rev. A 64 (2001) 012312-1-17
146. Harter W.G. Wave node dynamics and revival symmetry in quantum rotors J. Mol. Spec. 210 2001 166-182
147. Heller E.J. Bound-state eigenfunctions of classical chaotic Hamiltonian systems: scars of periodic orbits Phys. Rev. Lett. 53 1984 1515-1518
148. Kaplan L. Heller E.J. Linear and non-linear theory of eigenfunction scars Ann. Phys. 264 1998 171-206
149. Kaplan L. Heller E.J. Measuring scars of periodic orbits Phys. Rev. E 59 1999 6609-6628
150. Cooper F. Khare A. Sukhatme U. Supersymmetry and quantum mechanics Phys. Rep. 251 1995 267-385
151. Dutt R. Khare A. Sukhatme U. Supersymmetry, shape invariance, and exactly solvable potentials Am. J. Phys. 56 1988 163-168
152. Cooper F. Freedman B. Aspects of supersymmetric quantum mechanics Ann. Phys. 146 1983 262-288
153. Witten E. Dynamical breaking of supersymmetry Nucl. Phys. B 188 1981 513-554
154. Antoine J.-P. Gazeau J.-P. Monceau P. Klauder J.R. Penson K.A. Temporally stable coherent states for infinite well and Pöschl-Teller potentials J. Math. Phys. 42 2001 2349-2387
155. 2 well Eur. J. Phys. 24 2003 1-5
156. Banerji J. Agarwal G.W. Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states Phys. Rev. A 59 1999 4777-4783
157. Bluhm R. Kostelecký V.A. Atomic supersymmetry, Rydberg wave packets, and radial squeezed states Phys. Rev. A 1994 4628-4640 [arXiv:quant-ph/9508020]
158. Venugopalan A. Agarwal G.S. Superrevivals in the quantum dynamics of a particle confined in a finite square-well potential Phys. Rev. A 59 1999 1413-1421 [arXiv:quant-ph/9811012].
159. D.L. Aronstein, C.R. Stroud Jr., Analytical investigation of revival phenomena in the finite square-well potential, Phys. Rev. A 62 (2000) 022102-1-9.
160. Aronstein D.L. Stroud C.R.Jr. General series solution for finite square-well energy levels for use in wave-packet studies Am. J. Phys. 68 2000 943-949
161. Epstein S.T. Application of the Rayleigh-Schrödinger perturbation theory to the delta-function potential Am. J. Phys. 28 1960 495-496
162. Gettys W.E. Quantum theory of a square well plus delta function potential Am. J. Phys. 41 1973 670-677
163. Atkinson D. Crater H.W. An exact treatment of the Dirac δ-function in the Schrödinger equation Am. J. Phys. 43 1974 301-304
164. Lapidus I.R. One-dimensional hydrogen atom in an infinite square well Am. J. Phys. 50 1982 563-564
165. Lapidus I.R. Particle in a square well with a δ-function potential Am. J. Phys. 55 1987 172-174
166. Senn P. Time evolutions of quantum mechanical states in a symmetric double-well potential Am. J. Phys. 60 1992 228-231
167. Goldstein J. Lebiedzik C. Robinett R.W. Supersymmetric quantum mechanics: examples with Dirac δ functions Am. J. Phys. 62 1994 612-618
168. G.A. Vugalter, A.K. Das, V.A. Sorokin, Revivals in an infinite square well in the presence of a δ well, Phys. Rev. A 66 (2002) 012104-1-7.
169. J.P. Dowling, J. Gea-Banacloche, Evanescent light-wave atom mirrors, resonators, waveguides, and traps in: B. Bederson, H. Walther (Eds.), Adv. At. Mol. Opt. 37, Academic Press, San Diego, 1996, pp. 1-94.
170. Aminoff C.G. Steane A.M. Bouyer P. Desbiolles P. Dalibard J. Cohen-Tannoudji C. Cesium atoms bouncing in a stable gravitational cavity Phys. Rev. Lett. 71 1993 3083-3086
171. Roach T.M. Abele H. Boshier M.G. Grossman H.L. Zetie K.P. Hinds E.A. Realization of a magnetic mirror for cold atoms Phys. Rev. Lett. 75 1995 629-632
172. Szriftgiser P. Guéry-Odelin D. Arndt M. Dalibard J. Atomic wave diffraction and interference using temporal slits Phys. Rev. Lett. 77 1996 4-7
173. Chen W.-Y. Milburn G.J. Fractional quantum revivals in the atomic gravitational cavity Phys. Rev. A 51 1995 2328-2333
174. Gea-Banacloche J. A quantum bouncing ball Am. J. Phys. 67 1999 776-782
175. Vallée O. Comment on Ref. [149]. Am. J. Phys. 68 2000 672-673
176. Goodmanson D.M. A recursion relation for matrix elements of the quantum bouncer Am. J. Phys. 68 2000 866-868
177. Doncheski M.A. Robinett R.W. Expectation value analysis of wave packet solutions for the quantum bouncer: short-term classical and long-term revival behaviors Am. J. Phys. 69 2001 1084-1090 [arXiv:quant-ph/0307046]
178. Saif F. Alber G. Savichev V. Schleich W.P. Quantum revivals in a periodically driven gravitational cavity J. Opt. B 2 2000 668-671 [arXiv:quant-ph/0006041]
179. Saif F. Quantum recurrences: probe to study quantum chaos Phys. Rev. E 62 2000 6308-6311
180. Breit G. The propagation of Schroedinger waves in a uniform field of force Phys. Rev. 32 1928 273-276
181. V.V. Nesvizhevsky, et al., Measurement of quantum states of neutrons in the Earth's gravitational field, Phys. Rev. D 67 (2003) 102002-1-9.
182. B.O. Kerbikov, A.E. Kudryavtsev, V.A. Lensky, Neutron-antineutron oscillations in a trap revisited [arXiv:hep-ph/0306039].
183. Andrews M. Wave packets bouncing off walls Am. J. Phys. 66 1998 252-254
184. de la Torre L. Gori F. The bouncing bob: quasi-classical states Eur. J. Phys. 24 2003 253-259
185. A.C. de la Torre, H.O. M'artin, D. Goyeneche, Quantum diffusion on a cyclic one dimensional lattice, Phys. Rev. E 68 (2003) 031103-1-9 [arXiv:quant-ph/0304065].
186. Condon E.U. The physical pendulum in quantum mechanics Phys. Rev. 31 1928 891-894
187. Doncheski M.A. Robinett R.W. Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum Ann. Phys. 308 2003 578-598 [arXiv:quant-ph/0307079]. See also Ref. [162].
188. Ross J.C. Capel H.W. Fractional revivals of coherence in quantum mechanical oscillators Physica A 287 2000 217-258
189. Rozmej P. Arvieu R. Clones and other interference effects in the evolution of angular-momentum coherent states Phys. Rev. A 58 1998 4314-4329
190. Auzinsh M. The evolution and revival structure of angular momentum wave packets Can. J. Phys. 77 1999 491-503 [arXiv:physics/9905019] (Tutorial).
191. Tomsovic S. Lefebvre J.H. Can wave packet revivals occur in chaotic quantum systems? Phys. Rev. Lett. 79 1997 3629-3632
192. Berry M.V. Wilkinson M. Diabolical points in the spectra of triangles Proc. R. Soc. London, A 392 1984 15-43
193. Li W.-K. A particle in an isosceles right triangle J. Chem. Educ. 61 1984 1034
194. Robinett R.W. Isolated versus non-isolated periodic orbits in variants of the two-dimensional square and circular billiards J. Math. Phys. 40 1999 101-122
195. J. Mathews, R.L. Walker, Mathematical Methods of Physics, 2nd Edition, W. A. Benjamin, Menlo Park, 1970, pp. 237-239.
196. Jung C. An exactly soluble three-body problem in one-dimension Can. J. Phys. 58 1980 719-728
197. Richens P.J. Berry M.V. Pseudointegrable systems in classical and quantum mechanics Physica 2D 1981 495-512
198. Li W.-K. Blinder S.M. Particle in an equilateral triangle: exact solution of a nonseparable problem J. Chem. Educ. 64 1987 130-132
199. Doncheski M.A. Robinett R.W. Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals Ann. Phys. (New York) 299 2002 208-227 [arXiv:quant-ph/0307063]
200. Liboff R.L. The polygon quantum-billiard problem J. Math. Phys. 35 1994 596-607
201. Amar V. Pauri M. Scotti A. Schrödinger equation for convex plane polygons: a tiling method for the derivation of eigenvalues and eigenfunctions J. Math. Phys. 32 1991 2442-2449
202. Amar V. Pauri M. Scotti A. Schrödinger equation for convex plane polygons. II. a no-go theorem for plane waves representation of solutions J. Math. Phys. 34 1993 3343-3350
203. Liboff R.L. The hexagon quantum billiard J. Stat. Phys. 105 2001 389-402
204. R.W. Robinett, S. Heppelmann, Quantum wave-packet revivals in circular billiards, Phys. Rev. A 65 (2002) 062103-1-10 [arXiv:quant-ph/0307020].
205. Langer R.E. On the connection formulas and the solutions of the wave equation Phys. Rev. 51 1937 669-676
206. L.D. Landau, E.M. Lifschitz, Quantum Mechanics: Non-relativistic Theory, Pergamon Press, London, 1958, pp. 166-171.
207. Berry M.V. Mount K.E. Semiclassical approximations in wave mechanics Rep. Prog. Phys. 35 1972 315-397
208. Fröman N. Fröman P.O. Phase-integral Method 1996 Springer New York
209. Berry M.V. Ozorio de Almeida A.M. Semiclassical approximation of the radial equation with two-dimensional potentials J. Phys. A 6 1973 1451-1460
210. Robnik M. Quantising a generic family of billiards with analytic boundaries J. Phys. A 17 1984 1049-1074
211. Prosen T. Robnik M. Failure of semiclassical methods to predict individual energy levels J. Phys. A 26 1993 L37-L44
212. Main J. Weiberg K. Wunner G. ℏ expansion for the periodic orbit quantization by harmonic inversion Phys. Rev. E 58 1998 4436-4439
213. Friedrich H. Trost J. Accurate WKB wave functions for weakly attractive inverse square potentials Phys. Rev. A 59 1999 1683-1686
214. Bluhm R. Kostelecký V.A. Quantum defects and the long-term behavior of radial Rydberg wave packets Phys. Rev. A 50 1994 R4445-R4448 [arXiv:hep-ph/9410325].
215. Wals J. Fielding H.H. van Linden van den Heuvell H.B. The role of the quantum defect and of high-order dispersion in Rydberg wave packets Phys. Scr. T 58 1995 62-68
216. Robinett R.W. Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum Eur. J. Phys. 24 2003 231-243 [arXiv:quant-ph/0307035]
217. Yeazell J.A. Stroud Jr. C.R. Rydberg-atom wave packets localized in angular variables Phys. Rev. A 35 1987 2806-2809
218. Henle W.A. Ritsch H. Zoller P. Rydberg wave packets in many-electron atoms excited by short laser pulses Phys. Rev. A 36 1987 683-692
219. Grochmalicki J. Lewenstein M. Excitation of Rydberg wavepackets by short laser pulses J. Phys. B 21 1988 3285-3302
220. Nauenberg M. Quantum wave packets on Kepler elliptic orbits Phys. Rev. A 40 1989 1133-1136
221. Parker J. Stroud Jr. C.R. Population trapping in short-pulse laser ionization Phys. Rev. A 41 1990 1602-1608
222. Gaeta Z.D. Stroud Jr. C.R. Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom Phys. Rev. A 42 1990 6308-6313
223. Gaeta Z.D. Noel M.W. Stroud Jr. C.R. Excitation of the classical-limit state of an atom Phys. Rev. Lett. 73 1994 636-639
224. Suarez Barnes I.M. Nauenberg M. Nockleby M. Tomsovic S. Semiclassical theory of quantum propagation: the Coulomb potential Phys. Rev. Lett. 71 1993 1961-1964
225. Mallalieu M. Stroud Jr. C.R. Semiclassical dynamics of circular orbit Rydberg wave packets Phys. Rev. A 49 1994 2329-2339
226. Mallalieu M. Stroud Jr. C.R. Semiclassical theory of Rydberg-wave-packet interferometry Phys. Rev. A 51 1995 1827-1835
227. Bluhm R. Kostelecký V.A. Radial squeezed states and Rydberg wave packets Phys. Rev. A 48 1993 R4047-R4050 [arXiv:quant-ph/9508019]
228. Bluhm R. Kostelecký V.A. Elliptical squeezed states and Rydberg wave packets Phys. Rev. A 52 1995 2234-2244 [arXiv:quant-ph/9509010]
229. Bluhm R. Kostelecký V.A. Keplerian squeezed states and Rydberg wave packets Phys. Rev. A 53 1996 937-945 [arXiv:quant-ph/9510023].
230. Bluhm R. Kostelecký V.A. Tudose B. Revivals of Rydberg wave packets Phys. At. Nucl. 61 1998 1948-1953 [arXiv:quant-ph/9711073].
231. Carlsen H. Goscinski O. Dynamics of particles for circular Rydberg states Phys. Rev. A 59 1999 1063-1069
232. Delande D. Gay J.C. A new method for producing circular Rydberg states Europhys. Lett. 5 1988 303-308
233. Hare J. Gross M. Goy P. Circular atoms prepared by a new method of crossed electric and magnetic fields Phys. Rev. Lett. 61 1988 1938-1941
234. Gay J.-C. Delande D. Bommier A. Atomic quantum states with maximum localization on classical elliptical orbits Phys. Rev. A 39 1989 6587-6590
235. Penent F. Delande D. Gay J.C. Rydberg states of rubidium in crossed electric and magnetic fields Phys. Rev. 37 1988 4707-4719
236. Strehle M. Weichmann U. Gerber G. Femtosecond time-resolved Rydberg wave-packet dynamics in the two-electron system calcium Phys. Rev. A 58 1998 450-455
237. Wetzels A. Gürtler A. Muller H.G. Noordam L.D. The dynamics of a THz Rydberg wavepacket Eur. Phys. J. D 14 2001 157-165
238. G. Alber, Laser excitation of Stark-induced resonances, Phys. Rev. A 40 (1989) 1321-1329.
239. ten Wolde A. Noordam L.D. Lagendijk A. van Linden van den Heuvell H.B. Atomic electron wave packets in an electrical field Phys. Rev. A 40 1989 485-488
240. Noordam L.D. ten Wolde A. Lagendijk A. van Linden van den Heuvell H.B. Time dependence of an atomic electron wave function in an electrical field Phys. Rev. A 40 1989 6999-7006
241. Fielding H.H. Wals J. van der Zande W.J. van Linden van den Heuvell H.B. Rydberg-electron wave-packet dynamics in parallel electric and magnetic fields and evidence for stabilization Phys. Rev. A 51 1995 611-619
242. Naudeau M.L. Sukenik C.I. Bucksbaum P.H. Core scattering of Stark wave packets Phys. Rev. A 56 1997 636-639
243. Wals J. Fielding H.H. van Linden van den Heuvell H.V. Rydberg electron dynamics in external fields Mod. Phys. Lett. B 9 1995 1845-1871
244. Broers B. Christian J.F. Hoogenraad J.H. van der Zande W.J. van Linden van den Heuvell H.B. Noordam L.D. Time-resolved dynamics of electronic wave packets above the classical field-ionization threshold Phys. Rev. Lett. 71 1993 344-347
245. Christian J.F. Broers B. Hoogenraad J.H. van der Zande W.J. Noordam L.D. Rubidium electronic wave packets probed by a phase-sensitive pump-probe technique Opt. Commun. 103 1993 79-84
246. Broers B. Christian J.F. van Linden van den Heuvell H.B. Experimental investigation of rubidium atoms above the field-ionization limit using a time-resolved wave packet approach Phys. Rev. A 49 1994 2498-2507
247. Lankhuijzen G.M. Noordam L.D. Frequency- and time-resolved study of the dynamics of rubidium Rydberg wave packets in an electric field Phys. Rev. A 52 1995 2016-2028
248. E. Reinhold, W. Ubachs, Observation of coherent wave packets in a heavy Rydberg system, Phys. Rev. Lett. 88 (2002) 013001-1-4.
249. Bluhm R. Kosteleckỳ V.A. Tudose B. Revival structure of Stark wave packets Phys. Rev. A 55 1997 819-822 [arXiv:quant-ph/9608040]
250. Bowman R.M. Dantus M. Zewail A.H. Femtosecond transition-state spectroscopy of iodine: from strongly bound to repulsive surface dynamics Chem. Phys. Lett. 161 1989 297-302
251. Dantus M. Bowman R.M. Zewail A.H. Femtosecond laser observations of molecular vibration and rotation Nature 343 1990 737-739
252. Rosker M.J. Rose T.S. Zewail A.H. Femtosecond real-time dynamics of photofragment-trapping resonances on dissociative potential energy surfaces Chem. Phys. Lett. 146 1988 175-179
253. Rose T.S. Rosker M.J. Zewail A.H. Femtosecond real-time probing of reactions. IV. The reactions of alkali halides J. Chem. Phys. 91 1989 7415-7436
254. 1 state potential Chem. Phys. Lett. 172 1990 99-108
255. 2 Chem. Phys. Lett. 191 1992 639 644. See also Ref. [218].
256. 2 molecule Chem. Phys. Lett. 257 1996 365-373
257. 2 wavepacket dynamics Chem. Phys. 207 1996 331-354
258. + state Chem. Phys. Lett. 269 1997 1-8
259. 2 Phys. Rev. A 54 1996 306-313
260. 2 molecule Eur. Phys. J. D 4 1998 151-158
261. See, e.g., H. London (Ed.), Separation of Isotopes, George Newnes Limited, London, 1961.
262. Greenland P.T. Laser isotope separation Contemp. Phys. 31 1990 405-424
263. King W.H. Isotope Shifts in Atomic Spectra 1984 Plenum New York
264. Averbukh I.Sh. Vrakking M.J.J. Villeneuve D.M. Stolow A. Wave packet isotope separation Phys. Rev. Lett. 77 1996 3518-3521
265. M. Leibscher, I.Sh. Averbukh, Optimal control of wave-packet isotope separation, Phys. Rev. A 63 (2001) 043407-1-9.
266. I.Sh. Averbukh, Laser isotope separation by excitation of wavepackets, United States Patent 5827405 (October 27, 1998).
267. Grebenshchikov S.Yu. Beck C. Flöthmann H. Mordaunt D.H. Schinke R. Revivals in triatomic molecules: influence of mode mixing Chem. Phys. Lett. 271 1997 197-203
268. Meyer S. Engel V. Vibrational revivals and the control of photochemical reactions J. Phys. Chem. 101 1997 7749-7753
269. 2 vapor Phys. Rev. Lett. 34 1975 1299-1302
270. P.M. Felker, A.H. Zewail, Molecular structures from ultrafast coherence spectroscopy, in: J. Manz, L. Wöste (Eds.), Femtosecond Chemistry, Vol. 1, VCH, Weinheim, 1995, pp. 193-260.
271. Seideman T. Revival structure of aligned rotational wave packets Phys. Rev. Lett. 83 1999 4971-4974
272. 2, Phys. Rev. Lett. 87 (2001) 152902-1-4.
273. 2 molecules. I. Experimental results J. Chem. Phys. 116 2002 6567-6578
274. 2 molecules. II. Numerical modeling J. Chem. Phys. 116 2002 6579-6588
275. R.A. Bartels, T.C. Weinacht, N. Wagner, M. Baertschy, C.H. Greene, M.M. Murname, H.C. Kapteyn, Phase modulation of ultrashort light pulses using molecular rotational wave packets, Phys. Rev. Lett. 88 (2002) 013903-1-4.
276. Comstock M. Lozovoy V.V. Dantus M. Rotational wavepacket revivals for phase modulation of ultrafast pulses Chem. Phys. Lett. 372 2003 739-744
277. Althorpe S.C. Seideman T. Predictions of rotation-vibration effects in time-resolved photoelectron angular distributions J. Chem. Phys. 113 2000 7901-7910
278. T. Hansson, Cross-revival of molecular wave packets, Phys. Rev. A 61 (2000) 033404-1-7.
279. 60 molecule J. Phys. B 33 2000 1663-1674
280. Jaynes E.T. Cummings F.W. Comparison of quantum and semiclassical radiation theories with applications to the beam maser Proc. IEEE 51 1963 89-109
281. Stenholm S. Quantum theory of electromagnetic fields interacting with atoms and molecules Phys. Rep. 6 1973 1-122
282. Knight P.L. Milloni P.W. The Rabi frequency in optical spectra Phys. Rep. 66 1980 21-107
283. Yoo H.-I. Eberly J.H. Dynamical theory of an atom with two or three levels interacting with quantized cavity fields Phys. Rep. 118 1985 239-337
284. Barnett S.M. Filipowicz P. Javananinen J. Knight P.L. Meystre P. The Jaynes-Cummings model and beyond, in: Pike E.R. Sarkar S. (Eds.), Frontiers in Quantum Optics 1986 Adam Hilger Bristol
285. Cummings F.W. Stimulated emission of radiation in a single mode Phys. Rev. 140 1965 A1051-A1056
286. Meystre P. Quattropani A. Baltes H.P. Quantum mechanical approach to Rabi flipping Phys. Lett. A 49 1974 85-86
287. Eberly J.H. Narozhny N.B. Sanchez-Mondragon J.J. Periodic spontaneous collapse and revival in a simple quantum model Phys. Rev. Lett. 44 1980 1323-1326
288. Narozhny N.B. Sanchez-Mondragon J.J. Eberly J.H. Coherence versus incoherence: collapse and revival in a simple quantum model Phys. Rev. A 23 1981 236-247
289. Frahm J. Quantenmechanische Streuung der elektrischen Felstärke einer gestörten Resonator-Eigenschwingung Ann. Phys (Leipzig) 18 1966 205-208
290. Yoo H.-I. Sanchez-Mondragon J.J. Eberly J.H. Non-linear dynamics of the fermion-boson model: interference between revivals and the transition to irregularity J. Phys. A 14 1981 1383-1397
291. Fleischhauer M. Schleich W.P. Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes-Cummings model Phys. Rev. A 47 1993 4258-4269
292. Filipowicz P. Quantum revivals in the Jaynes-Cummings model J. Phys. A 19 1986 3785-3795
293. Cahill K.E. Glauber R.J. Density operators and quasiprobability distributions Phys. Rev. 177 1969 1882-1902
294. Eiselt J. Risken H. Calculation of quasiprobabilities for the damped Jaynes-Cummings model Opt. Commun. 72 1989 351-355
295. Eiselt J. Risken H. Quasiprobability distributions for the Jaynes-Cummings model with cavity damping Phys. Rev. A 43 1991 346-360
296. Rempe G. Walter H. Klein N. Observation of quantum collapse and revival in a one-atom maser Phys. Rev. Lett. 58 1987 353-356 See also F. Diedrich, J. Krause, G. Rempe, M.O. Scully, H. Walther, Laser experimentswith single atoms as a test of basic physics, IEEE J. Quant. Electron. 24 (1988) 1314-1319
297. Meschede D. Walther H. Müller G. One-atom maser Phys. Rev. Lett. 54 1985 511-554
298. Brune M. Schmidt-Kaler F. Maali A. Dreyer J. Hagley E. Raimond J.M. Haroche S. Quantum Rabi oscillations: a direct test of field quantization in a cavity Phys. Rev. Lett. 76 1996 1800-1805
299. Wright E.M. Meystre P. Collapse and revival in the micromaser Opt. Lett. 14 1989 177-179
300. Averbukh I.Sh. Fractional revivals in the Jaynes-Cummings model Phys. Rev. A 46 1992 R2205-R2208
301. Góra P.F. Jedrzejek C. Superstructures, fractional revivals, and optical Schrödinger-cat states in the Jaynes-Cummings model Phys. Rev. A 48 1993 3291-3300
302. Góra P.F. Jedrzejek C. Revivals and superstructures in the Jaynes-Cummings model with a small number of photons Phys. Rev. A 49 1994 3046-3056
303. Cirac J.I. Blatt R. Parkins A.S. Zoller P. Quantum collapse and revival in the motion of a single trapped ion Phys. Rev. A 49 1994 1202-1207
304. Quang T. Knight P.L. Bužek V. Quantum collapses and revivals in an optical cavity Phys. Rev. A 44 1991 6092-6096
305. Gea-Banacloche J. Collapse and revival of the state vector in the Jaynes-Cummings model: an example of state preparation by a quantum apparatus Phys. Rev. Lett. 65 1990 3385-3388
306. Gea-Banacloche J. Atom- and field-state evolution in the Jaynes-Cummings model for large initial fields Phys. Rev. A 44 1991 5913-5931
307. Phoenix S.J.D. Knight P.L. Comment on Ref. [261] Phys. Rev. Lett. 66 1991 2833
308. Phoenix S.J.D. Knight P.L. Establishment of an entangled atom-field state in the Jaynes-Cummings model Phys. Rev. A 44 1991 6023-6029
309. Bužek V. Moya-Cessa H. Knight P.L. Phoenix S.J.D. Schrödinger-cat states in the resonant Jaynes-Cummings model: collapse and revival of oscillations of the photon-number distribution Phys. Rev. A 45 1992 8190-8203
310. Knight P.L. Shore B.W. Schrödinger-cat states of the electromagnetic field and multi-level atoms Phys. Rev. A 48 1993 642-655
311. Buck B. Sukumar S.V. Exactly soluble model of atom-phonon coupling showing periodic decay and revival Phys. Lett. 81 A 1981 132-135
312. Marzlin K.-P. Audretsch J. Collapse and revival of ultracold atoms in a microwave cavity and of photons in parametric down-conversion Phys. Rev. A 57 1998 1333-1337 See also Ref. [267]
313. Drobný G. Jex I. Collapses and revivals in the energy exchange in the process of k-photon down-conversion with quantized pump Phys. Rev. A 45 1992 1816-1821
314. Domokos P. Kiss T. Janszky J. Zucchetti A. Kis Z. Vogel W. Collapse and revival in the vibronic dynamics of laser-driven diatomic molecules Chem. Phys. Lett. 322 2000 255-262
315. Meekhof D.M. Monroe C. King B.E. Itano W.M. Wineland D.J. Generation of nonclassical motional states of a trapped atom Phys. Rev. Lett. 76 1996 1796-1799
316. Raithel G. Phillips W.D. Rolston S.L. Collapse and revivals of wave packets in optical lattices Phys. Rev. Lett. 81 1998 3615-3618
317. Raithel G. Phillips W.D. Rolston S.L. Decay of atomic wave-packet motion in optical lattices Fortschr. Phys. 46 1998 791-799
318. Buchkremer F.B.J. Dumke R. Levsen H. Birkl G. Ertmer W. Wave packet echoes in the motion of trapped atoms Phys. Rev. Lett. 85 2000 3121-3124
319. Parkins A.S. Walls D.F. The physics of trapped dilute-gas Bose-Einstein condensates Phys. Rep. 303 1998 1-80
320. Dunningham J.A. Collett M.J. Walls D.F. Quantum state of a trapped Bose-Einstein condensate Phys. Lett. A 245 1998 49-54
321. Wright E.M. Wong T. Collett M.J. Tan S.M. Walls D.F. Collapses and revivals in the interference between two Bose-Einstein condensates formed in small atomic samples Phys. Rev. A 56 1997 591-602
322. Imamoglu A. Lewenstein M. You L. Inhibition of coherence in trapped Bose-Einstein condensates Phys. Rev. Lett. 78 1997 2511-2514 The possibility of collapse and revival times in the context of Josephson junctions hasalso been discussed, as in Ref. [276].
323. Sols F. Randomization of the phase after suppression of the Josephson coupling Physica B 194-196 1994 1389-1390
324. M.O. Scully, M. Suhail Zubairy, Quantum Optics, Cambridge University Press, Cambridge, 1997, pp. 79-95.
325. K. Patorski, The self-imaging phenomenon and its applications, in: E. Wolf (Ed.), Progress in Optics, Vol. 27, North Holland, Amsterdam, 1989, pp. 1-108.
326. Fox Talbot W.H. Facts related to optical science. No. IV Phil. Mag. 9 1836 401-405
327. Rayleigh L. On copying diffraction-gratings and on some phenomena connected therewith Phil. Mag. 11 1881 196-205
328. Winthrop J.T. Worthington C.R. Theory of Fresnel images I. Plane periodic objects in monochromatic light J. Opt. Soc. Am. 55 1965 373-381
329. Berry M.V. Klein S. Integer, fractional, and fractal Talbot effects J. Mod. Opt. 43 1996 2139-2164
330. Banaszek K. Wódkiewicz K. Schleich W.P. Fractional Talbot effect in phase space: a compact summation formula Opt. Express 2 1998 169-172
331. Banaszek K. Wódkiewicz K. Schleich W.P. Fractional dynamics in phase space Laser Phys. 10 2000 123-126
332. Berry M.V. Bodenschatz E. Caustics, multiply reconstructed by Talbot interference J. Mod. Opt. 46 1999 349-365
333. Berry M. Marzoli I. Schleich W.P. Quantum carpets, carpets of light Phys. World 14 6 2001 39-44
334. Clauser J.F. Dowling J.P. Factoring integers with Young's N-slit interferometer Phys. Rev. A 53 1996 4587-4590
335. Rohwedder B. Atom optical elements based on near-field grating sequences Fortschr. Phys. 47 1999 883-911
336. Clauser J.F. Li S. Talbot-von Lau atom interferometry with cold slow potassium Phys. Rev. A 49 1994 R2213-R2216
337. Chapman M.S. Ekstrom C.R. Hammond T.D. Schmiedmayer J. Tannian B.E. Wehinger S. Pritchard D.E. Near-field imaging of atom diffraction gratings: the atomic Talbot effect Phys. Rev. A 51 1995 R14-R17
338. Nowak S. Kurtsiefer Ch. Pfau T. David C. High-order Talbot fringes for atomic matter waves Opt. Lett. 22 1997 1430-1432
339. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, A. Zeilinger, Matter-wave interferometer for large molecules, Phys. Rev. Lett. 88 (2002) 100404-1-4.
340. Bryngdahl O. Image formation using self-imaging techniques J. Opt. Soc. Am. 63 1973 416-418
341. Ulrich R. Image formation by phase coincidences in optical waveguides Opt. Commun. 13 1975 259-264
342. Ulrich R. Ankele G. Self-imaging in homogeneous planar optical waveguides Appl. Phys. Lett. 27 1975 337-339
343. Ulrich R. Kamiya T. Resolution of self-images in planar optical waveguides J. Opt. Soc. Am. 68 1978 583-592
344. O. Bryngdahl, Self-imaging with an optical tunnel for image formation, United States Patent 3832029 (August 27,1974)
345. R. Ulrich, Self imaging system using a waveguide, United States Patent 4087159 (May 2, 1978).
346. Ovchinnikov Yu.B. Revivals of light in a planar metal waveguide Opt. Commun. 182 2000 35-43
347. Yu.B. Ovchinnikov, T. Pfau, Revivals and oscillations of the momentum of light in a planar multimode waveguide, Phys. Rev. Lett. 87 (2001) 123901-1-4.
348. Fischer B. Ulrich R. Self-imaging in a planar X-ray waveguide Appl. Phys. Lett. 36 1980 356-358
349. Simon A. Ulrich R. Fiber-optical interferometer Appl. Phys. Lett. 31 1977 77-79
350. Heaton J.M. Jenkins R.M. Wright D.R. Parker J.T. Birbeck J.C.H. Hilton K.P. Novel 1-to-N integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides Appl. Phys. Lett. 61 1992 1754-1756
351. Zülicke U. Bluhm R. Kostelecký V.A. MacDonald A.H. Edge-magnetoplasmon wave-packet revivals in the quantum-Hall effect Phys. Rev. B 55 1997 9186-9800
352. Shin J.-Y. Lee H.-W. Quantum tunneling, dynamical symmetry, and quantum revival Phys. Rev. E 53 1996 3096-3100
353. Breslin J.K. Holmes C.A. Milburn G.J. Quantum signatures of chaos in the dynamics of a trapped ion Phys. Rev. A 56 1997 3022-3027
354. F. Saif, M. Fortunato, Quantum revivals in periodically driven systems close to nonlinear resonances, Phys. Rev. A 65 (2001) 013401-1-5.
355. Buchleitner A. Delande D. Zakrzewski J. Non-dispersive wave packets in periodically driven quantum systems Phys. Rep. 368 2002 409-547
356. Marcus C.M. Rimberg A.J. Westervelt R.M. Hopkins P.F. Gossard A.C. Conductance fluctuations and chaotic scattering in ballistic microstructures Phys. Rev. Lett. 69 1992 506-509
357. Friedman N. Kaplan A. Carasso D. Davidson N. Observation of chaotic and regular dynamics in atom-optics billiards Phys. Rev. Lett. 86 2001 1518-1521
358. Stöckmann H.-J. Stein J. Quantum chaos in billiards studied by microwave absorption Phys. Rev. Lett. 64 1990 2215-2218
359. Doron E. Smilansky U. Frenkel A. Experimental demonstration of chaotic scattering of microwaves Phys. Rev. Lett. 65 1990 3072-3075
360. Sridhar S. Heller E.J. Physical and numerical experiments on the wave mechanics of classically chaotic systems Phys. Rev. A 46 1992 R1728-R1731
361. Balian R. Bloch C. Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillations Ann. Phys. 69 1972 76-160
362. Reimann S.M. Brack M. Magner A.G. Murthy M.V.N. Applications of classical periodic orbit theory to circular billiards with small scattering centers Surf. Rev. Lett. 3 1996 19-23
363. Robinett R.W. Energy eigenvalues and periodic orbits for the circular disk or annular infinite well Surf. Rev. Lett. 5 1998 519-526
364. Robinett R.W. Periodic orbit theory analysis of the circular disk or annular billiard: nonclassical effects and the distribution of energy eigenvalues Am. J. Phys. 67 1999 67-77