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Volumn 72, Issue 9, 2004, Pages 1183-1192

Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets

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Indexed keywords


EID: 4544273266     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1767100     Document Type: Article
Times cited : (37)

References (67)
  • 1
    • 0003985181 scopus 로고    scopus 로고
    • Brooks/Cole, Belmont, CA, 5th ed.
    • J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Brooks/Cole, Belmont, CA, 2004), 5th ed.; G. R. Fowles and G. L. Cassiday, Analytical Mechanics (Harcourt Brace, Fort Worth, 1999), 6th ed.; A. P. Arya, Introduction to Classical Mechanics (Prentice-Hall, Upper Saddle River, NJ, 1998), 2nd ed.
    • (2004) Classical Dynamics of Particles and Systems
    • Marion, J.B.1    Thornton, S.T.2
  • 2
    • 0003835723 scopus 로고    scopus 로고
    • Harcourt Brace, Fort Worth, 6th ed.
    • J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Brooks/Cole, Belmont, CA, 2004), 5th ed.; G. R. Fowles and G. L. Cassiday, Analytical Mechanics (Harcourt Brace, Fort Worth, 1999), 6th ed.; A. P. Arya, Introduction to Classical Mechanics (Prentice-Hall, Upper Saddle River, NJ, 1998), 2nd ed.
    • (1999) Analytical Mechanics
    • Fowles, G.R.1    Cassiday, G.L.2
  • 3
    • 0008494867 scopus 로고    scopus 로고
    • Prentice-Hall, Upper Saddle River, NJ, 2nd ed.
    • J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Brooks/Cole, Belmont, CA, 2004), 5th ed.; G. R. Fowles and G. L. Cassiday, Analytical Mechanics (Harcourt Brace, Fort Worth, 1999), 6th ed.; A. P. Arya, Introduction to Classical Mechanics (Prentice-Hall, Upper Saddle River, NJ, 1998), 2nd ed.
    • (1998) Introduction to Classical Mechanics
    • Arya, A.P.1
  • 5
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932).
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.1
  • 6
    • 84931510621 scopus 로고
    • The Wigner representation of quantum mechanics
    • V. I. Tatarskiǐ, "The Wigner representation of quantum mechanics," Sov. Phys, Usp. 26, 311-327 (1983).
    • (1983) Sov. Phys, Usp. , vol.26 , pp. 311-327
    • Tatarskiǐ, V.I.1
  • 7
    • 0001555225 scopus 로고
    • Wigner's function and other distribution functions in mock phase space
    • N. L. Balaczs and B. K. Jennings, "Wigner's function and other distribution functions in mock phase space," Phys. Rep. 105, 347-391 (1984).
    • (1984) Phys. Rep. , vol.105 , pp. 347-391
    • Balaczs, N.L.1    Jennings, B.K.2
  • 8
    • 0001452799 scopus 로고
    • Quantum collision theory with phase-space distributions
    • P. Carruthers and F. Zachariasen, "Quantum collision theory with phase-space distributions," Rev. Mod. Phys. 55, 245-285 (1983).
    • (1983) Rev. Mod. Phys. , vol.55 , pp. 245-285
    • Carruthers, P.1    Zachariasen, F.2
  • 10
    • 0000532470 scopus 로고
    • A tomographic approach to Wigner's function
    • J. Bertrand and P. Bertrand, "A tomographic approach to Wigner's function," Found. Phys. 17, 397-405 (1987).
    • (1987) Found. Phys. , vol.17 , pp. 397-405
    • Bertrand, J.1    Bertrand, P.2
  • 11
    • 0004837979 scopus 로고
    • Canonical transformations in quantum mechanics
    • Y. S. Kim and E. P. Wigner, "Canonical transformations in quantum mechanics," Am. J. Phys. 58, 439-448 (1990).
    • (1990) Am. J. Phys. , vol.58 , pp. 439-448
    • Kim, Y.S.1    Wigner, E.P.2
  • 12
    • 0039513201 scopus 로고
    • Phase space picture of quantum mechanics: Group theoretical approach
    • World Scientific, Singapore
    • Y. S. Kim and M. E. Noz, "Phase space picture of quantum mechanics: Group theoretical approach," in Lecture Notes in Physics Series (World Scientific, Singapore, 1990), Vol. 40.
    • (1990) Lecture Notes in Physics Series , vol.40
    • Kim, Y.S.1    Noz, M.E.2
  • 13
    • 4243870641 scopus 로고
    • Theory and application of the quantum phase-space distribution functions
    • H.-W. Lee, "Theory and application of the quantum phase-space distribution functions," Phys. Rep. 259, 147-211 (1995).
    • (1995) Phys. Rep. , vol.259 , pp. 147-211
    • Lee, H.-W.1
  • 14
    • 0032020166 scopus 로고    scopus 로고
    • The Weyl representation in classical and quantum mechanics
    • A. M. Ozorio de Almeida, "The Weyl representation in classical and quantum mechanics," Phys. Rep. 296, 265-342 (1998).
    • (1998) Phys. Rep. , vol.296 , pp. 265-342
    • De Almeida, A.M.O.1
  • 15
    • 0005268501 scopus 로고
    • Quantum mechanical distribution functions: Conditions for uniqueness
    • R. F. O'Connell and E. P. Wigner, "Quantum mechanical distribution functions: Conditions for uniqueness," Phys. Lett. A 83, 145-148 (1981).
    • (1981) Phys. Lett. A , vol.83 , pp. 145-148
    • O'Connell, R.F.1    Wigner, E.P.2
  • 16
    • 3542994375 scopus 로고
    • New interpretation of the scalar product in Hubert space
    • R. F. O'Connell and A. K. Rajagopal, ''New interpretation of the scalar product in Hubert space," Phys. Rev. Lett. 48, 525-526 (1982).
    • (1982) Phys. Rev. Lett. , vol.48 , pp. 525-526
    • O'Connell, R.F.1    Rajagopal, A.K.2
  • 17
    • 33646651016 scopus 로고
    • Operational approach to phase-space measurements in quantum mechanics
    • R. F. O'Connell and D. F. Walls, "Operational approach to phase-space measurements in quantum mechanics," Nature (London) 312, 257-258 (1984).
    • (1984) Nature (London) , vol.312 , pp. 257-258
    • O'Connell, R.F.1    Walls, D.F.2
  • 18
    • 24544456897 scopus 로고
    • Area of overlap and interference in phase space versus Wigner pseudoprobabilities
    • W. Schleich, D. F. Walls, and J. A. Wheeler, "Area of overlap and interference in phase space versus Wigner pseudoprobabilities," Phys. Rev. A 38, 1177-1186 (1988).
    • (1988) Phys. Rev. A , vol.38 , pp. 1177-1186
    • Schleich, W.1    Walls, D.F.2    Wheeler, J.A.3
  • 19
    • 0000056091 scopus 로고
    • Wigner's phase space function and atomic structure I. The hydrogen atom ground state
    • J. P. Dahl and M. Springborg, "Wigner's phase space function and atomic structure I. The hydrogen atom ground state," Mol. Phys. 47, 1001-1019 (1982); M. Springborg and J. P. Dahl, "Wigner's phase space and atomic structure II. Ground states for closed-shell atoms," Phys. Rev. A 36, 1050-1062 (1987).
    • (1982) Mol. Phys. , vol.47 , pp. 1001-1019
    • Dahl, J.P.1    Springborg, M.2
  • 20
    • 0001120598 scopus 로고
    • Wigner's phase space and atomic structure II. Ground states for closed-shell atoms
    • J. P. Dahl and M. Springborg, "Wigner's phase space function and atomic structure I. The hydrogen atom ground state," Mol. Phys. 47, 1001-1019 (1982); M. Springborg and J. P. Dahl, "Wigner's phase space and atomic structure II. Ground states for closed-shell atoms," Phys. Rev. A 36, 1050-1062 (1987).
    • (1987) Phys. Rev. A , vol.36 , pp. 1050-1062
    • Springborg, M.1    Dahl, J.P.2
  • 21
    • 0002872891 scopus 로고
    • Dynamical equations for the Wigner functions
    • edited by J. Hinze (Plenum, New York)
    • J. P. Dahl, "Dynamical equations for the Wigner functions," in Energy Storage and Redistribution in Molecules, edited by J. Hinze (Plenum, New York, 1983), pp. 557-572.
    • (1983) Energy Storage and Redistribution in Molecules , pp. 557-572
    • Dahl, J.P.1
  • 22
    • 0013432092 scopus 로고
    • Wigner's phase space function and the bond in LiH
    • M. Springborg, "Wigner's phase space function and the bond in LiH," Theor. Chim. Act (Berl.) 63, 349-356 (1983).
    • (1983) Theor. Chim. Act (Berl.) , vol.63 , pp. 349-356
    • Springborg, M.1
  • 23
    • 36549097585 scopus 로고
    • The Morse oscillator in position space, momentum space, and phase space
    • J. P. Dahl and M. Springborg, "The Morse oscillator in position space, momentum space, and phase space," J. Chem. Phys. 88, 4535-4537 (1988).
    • (1988) J. Chem. Phys. , vol.88 , pp. 4535-4537
    • Dahl, J.P.1    Springborg, M.2
  • 24
    • 17344372775 scopus 로고
    • Modified spectral method in phase space: Calculation of the Wigner function. I. Fundamentals
    • M. Hug, C. Menke, and W. P. Schleich, "Modified spectral method in phase space: Calculation of the Wigner function. I. Fundamentals," Phys. Rev. A 57, 3188-3205 (1988); "Modified spectral method in phase space; Calculation of the Wigner function. II. Generalizations," ibid. 57, 3188-3205 (1988).
    • (1988) Phys. Rev. A , vol.57 , pp. 3188-3205
    • Hug, M.1    Menke, C.2    Schleich, W.P.3
  • 25
    • 17344372775 scopus 로고
    • Modified spectral method in phase space; Calculation of the Wigner function. II. Generalizations
    • M. Hug, C. Menke, and W. P. Schleich, "Modified spectral method in phase space: Calculation of the Wigner function. I. Fundamentals," Phys. Rev. A 57, 3188-3205 (1988); "Modified spectral method in phase space; Calculation of the Wigner function. II. Generalizations," ibid. 57, 3188-3205 (1988).
    • (1988) Phys. Rev. A , vol.57 , pp. 3188-3205
  • 26
    • 0348250331 scopus 로고
    • Wave functions rotated in phase space
    • J. Snygg, "Wave functions rotated in phase space," Am. J. Phys. 45, 58-60 (1977).
    • (1977) Am. J. Phys. , vol.45 , pp. 58-60
    • Snygg, J.1
  • 27
    • 84955046370 scopus 로고
    • Wigner distribution for angle coordinates in quantum mechanics
    • N. Mukunda, "Wigner distribution for angle coordinates in quantum mechanics," Am. J. Phys. 47, 192-187 (1979).
    • (1979) Am. J. Phys. , vol.47 , pp. 192-1187
    • Mukunda, N.1
  • 28
    • 0003218672 scopus 로고
    • The Wigner function: I. The physical interpretation
    • S. Stenholm, "The Wigner function: I. The physical interpretation," Eur. J. Phys. 1, 244-248 (1980).
    • (1980) Eur. J. Phys. , vol.1 , pp. 244-248
    • Stenholm, S.1
  • 29
    • 4544289086 scopus 로고
    • Solution of the Schroedinger equation for a system excited by a time Dirac pulse of potential. An example of the connection with the classical limit through a particular smoothing of the Wigner function
    • G. Mourgues, J. C. Andrieux, and M. R. Feix, "Solution of the Schroedinger equation for a system excited by a time Dirac pulse of potential. An example of the connection with the classical limit through a particular smoothing of the Wigner function," Eur. J. Phys. 5, 112-118 (1984).
    • (1984) Eur. J. Phys. , vol.5 , pp. 112-118
    • Mourgues, G.1    Andrieux, J.C.2    Feix, M.R.3
  • 30
    • 0043218528 scopus 로고
    • On the Wigner transforms of some simple systems and their semiclassical interpretations
    • M. Casas, H. Krivine, and J. Martorell, "On the Wigner transforms of some simple systems and their semiclassical interpretations," Eur. J. Phys. 12, 105-111 (1991).
    • (1991) Eur. J. Phys. , vol.12 , pp. 105-111
    • Casas, M.1    Krivine, H.2    Martorell, J.3
  • 31
    • 0032391973 scopus 로고    scopus 로고
    • Correlation coefficient for incompatible observables of the quantum harmonic oscillator
    • R. A. Campos, "Correlation coefficient for incompatible observables of the quantum harmonic oscillator," Am. J. Phys. 66, 712-718 (1998).
    • (1998) Am. J. Phys. , vol.66 , pp. 712-718
    • Campos, R.A.1
  • 34
  • 37
    • 0001552901 scopus 로고
    • Bilder elementarer Quantenmechanik
    • W. Kinzel, "Bilder elementarer Quantenmechanik," Phys. B1. 51, 1190-1191 (1995).
    • (1995) Phys. B1. , vol.51 , pp. 1190-1191
    • Kinzel, W.1
  • 38
    • 0040955204 scopus 로고    scopus 로고
    • Quantum fractals in boxes
    • M. V. Berry, "Quantum fractals in boxes," J. Phys. A 29, 6617-6629 (1996).
    • (1996) J. Phys. A , vol.29 , pp. 6617-6629
    • Berry, M.V.1
  • 39
    • 0031557853 scopus 로고    scopus 로고
    • Spacetime structures in simple quantum systems
    • F. Großmann, J.-M. Rost, and W. P. Schleich, "Spacetime structures in simple quantum systems," J. Phys. A 30, L277-L283 (1997).
    • (1997) J. Phys. A , vol.30
    • Großmann, F.1    Rost, J.-M.2    Schleich, W.P.3
  • 40
    • 0040453619 scopus 로고    scopus 로고
    • Das Teilchen im Kasten: Strukturen in der Wahrscheinlichkeitsdichte
    • translated as
    • P. Stifter, C. Leichtle, W. P. Schleich, and J. Marklov, "Das Teilchen im Kasten: Strukturen in der Wahrscheinlichkeitsdichte," translated as "The particle in a box: Structures in the probability density," Z. Naturforsch., A: Phys. Sci. 52, 377-385 (1997).
    • (1997) Z. Naturforsch., A: Phys. Sci. , vol.52 , pp. 377-385
    • Stifter, P.1    Leichtle, C.2    Schleich, W.P.3    Marklov, J.4
  • 43
    • 0033579253 scopus 로고    scopus 로고
    • Quantum revivals and carpets in some exactly solvable systems
    • arXiv:quant-ph/9902039
    • W. Loinaz and T. J. Newman, "Quantum revivals and carpets in some exactly solvable systems," J. Phys. A 32, 8889-8895 (1999), arXiv:quant-ph/9902039.
    • (1999) J. Phys. A , vol.32 , pp. 8889-8895
    • Loinaz, W.1    Newman, T.J.2
  • 44
    • 0033607380 scopus 로고    scopus 로고
    • Unravelling quantum carpets: A travelling wave approach
    • arXiv:quant-ph/9906107
    • M. J. W. Hall, M. S. Reineker, and W. P. Schleich, "Unravelling quantum carpets: a travelling wave approach," J. Phys. A 32, 8275-8291 (1999); arXiv:quant-ph/9906107.
    • (1999) J. Phys. A , vol.32 , pp. 8275-8291
    • Hall, M.J.W.1    Reineker, M.S.2    Schleich, W.P.3
  • 45
    • 4243711354 scopus 로고    scopus 로고
    • Multimode interference: Highly regular pattern formation in quantum wave-packet evolution
    • A. E. Kaplan, I. Marzoli, W. E. Lamb, Jr., and W. P. Schleich, "Multimode interference: Highly regular pattern formation in quantum wave-packet evolution," Phys. Rev. A 61, 032101-1-032101-6 (2000).
    • (2000) Phys. Rev. A , vol.61 , pp. 321011-321016
    • Kaplan, A.E.1    Marzoli, I.2    Lamb Jr., W.E.3    Schleich, W.P.4
  • 46
    • 0442307154 scopus 로고    scopus 로고
    • Quantum carpets woven by Wigner functions
    • O. M. Friesch, I. Marzoli, and W. P. Schleich, "Quantum carpets woven by Wigner functions," New J. Phys. 2, 4.1-4.11 (2000), (http://www.iop.org/ EJ/journal/JNP). Video sequences of time-dependent Wigner function for the infinite well are available at this Web site.
    • (2000) New J. Phys. , vol.2
    • Friesch, O.M.1    Marzoli, I.2    Schleich, W.P.3
  • 47
    • 0030537230 scopus 로고    scopus 로고
    • The evolution and revival structure of localized quantum wave packets
    • arXiv:quant-ph/9510029
    • R. Bluhm, V. A. Kostelecký, and J. Porter, "The evolution and revival structure of localized quantum wave packets," Am. J. Phys. 64, 944-953 (1996); arXiv:quant-ph/9510029.
    • (1996) Am. J. Phys. , vol.64 , pp. 944-953
    • Bluhm, R.1    Kostelecký, V.A.2    Porter, J.3
  • 48
    • 0442328987 scopus 로고    scopus 로고
    • Quantum wave packet revivals
    • arXiv:quant-ph/0401031
    • R. W. Robinett, "Quantum wave packet revivals," Phys. Rep. 392, 1-119 (2004); arXiv:quant-ph/0401031.
    • (2004) Phys. Rep. , vol.392 , pp. 1-119
    • Robinett, R.W.1
  • 49
    • 84862417683 scopus 로고    scopus 로고
    • See (www.arxiv.org/abs/quant-ph/0312086).
  • 50
    • 33646659831 scopus 로고    scopus 로고
    • See EPAPS Document No. E-AJPIAS-72-020408 for additional materials. A direct link to this document may be found in the online article's HTML reference section. The document may also be reached via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more information
    • See EPAPS Document No. E-AJPIAS-72-020408 for additional materials. A direct link to this document may be found in the online article's HTML reference section. The document may also be reached via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more information.
  • 51
    • 33646653631 scopus 로고    scopus 로고
    • note
    • H(x,p;t). This quasi-probability density, however, does not give the correct marginal distributions as in Eqs. (7a) and (7b).
  • 52
    • 0001218355 scopus 로고
    • When is the Wigner quasi-probability density nonnegative?
    • R. L. Hudson, "When is the Wigner quasi-probability density nonnegative?" Rep. Math. Phys. 6, 249-252 (1974); F. Soto and P. Claverie, "When is the Wigner function of multi-dimensional systems nonnegative?" J. Math. Phys. 24, 97-100 (1983).
    • (1974) Rep. Math. Phys. , vol.6 , pp. 249-252
    • Hudson, R.L.1
  • 53
    • 36749120013 scopus 로고
    • When is the Wigner function of multi-dimensional systems nonnegative?
    • R. L. Hudson, "When is the Wigner quasi-probability density nonnegative?" Rep. Math. Phys. 6, 249-252 (1974); F. Soto and P. Claverie, "When is the Wigner function of multi-dimensional systems nonnegative?" J. Math. Phys. 24, 97-100 (1983).
    • (1983) J. Math. Phys. , vol.24 , pp. 97-100
    • Soto, F.1    Claverie, P.2
  • 55
    • 0347088560 scopus 로고
    • Simple Schrödinger wave functions which simulate classical radiating systems
    • One of the earliest pedagogical visualizations of the time dependence of such a two-state system is by C. Dean, "Simple Schrödinger wave functions which simulate classical radiating systems," Am. J. Phys. 27, 161-163 (1959).
    • (1959) Am. J. Phys. , vol.27 , pp. 161-163
    • Dean, C.1
  • 56
    • 0442307139 scopus 로고
    • Continuity, determinism, and reality
    • M. Born, "Continuity, determinism, and reality," Kgl. Danske Videns. Sels. Mat.-fys. Medd. 30(2), 1-26 (1955), Bom was addressing concerns made by Einstein in "Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik," in Scientific Papers Presented to Max Born (Oliver and Boyd, Edinburgh, 1953), pp. 33-40.
    • (1955) Kgl. Danske Videns. Sels. Mat.-fys. Medd. , vol.30 , Issue.2 , pp. 1-26
    • Born, M.1
  • 57
    • 0142205203 scopus 로고
    • Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik
    • Oliver and Boyd, Edinburgh
    • M. Born, "Continuity, determinism, and reality," Kgl. Danske Videns. Sels. Mat.-fys. Medd. 30(2), 1-26 (1955), Bom was addressing concerns made by Einstein in "Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik," in Scientific Papers Presented to Max Born (Oliver and Boyd, Edinburgh, 1953), pp. 33-40.
    • (1953) Scientific Papers Presented to Max Born , pp. 33-40
  • 58
    • 0038575078 scopus 로고    scopus 로고
    • Wave packet construction in two-dimensional quantum billiards; Blueprints for the square, equilateral triangle, and circular cases
    • arXiv:quant-ph/0307070
    • M. A. Doncheski, S. Heppelmann, R. W. Robinett, and D. C. Tussey, "Wave packet construction in two-dimensional quantum billiards; Blueprints for the square, equilateral triangle, and circular cases," Am. J. Phys. 71, 541-557 (2003); arXiv:quant-ph/0307070.
    • (2003) Am. J. Phys. , vol.71 , pp. 541-557
    • Doncheski, M.A.1    Heppelmann, S.2    Robinett, R.W.3    Tussey, D.C.4
  • 59
    • 0034380364 scopus 로고    scopus 로고
    • Visualizing the collapse and revival of wave packets in the infinite square well using expectation values
    • arXiv:quant-ph/0307041
    • R. W. Robinett, "Visualizing the collapse and revival of wave packets in the infinite square well using expectation values," Am. J. Phys. 68, 410-442 (2000); arXiv:quant-ph/0307041.
    • (2000) Am. J. Phys. , vol.68 , pp. 410-442
    • Robinett, R.W.1
  • 60
    • 0001196732 scopus 로고
    • Exact solutions for time-dependent phenomena in quantum mechanics
    • M. Kleber, "Exact solutions for time-dependent phenomena in quantum mechanics;" Phys. Rep. 236, 331-393 (1994).
    • (1994) Phys. Rep. , vol.236 , pp. 331-393
    • Kleber, M.1
  • 61
    • 0032345922 scopus 로고    scopus 로고
    • Wave packets bouncing off walls
    • M. Andrews, "Wave packets bouncing off walls," Am. J. Phys. 66, 252-254 (1998).
    • (1998) Am. J. Phys. , vol.66 , pp. 252-254
    • Andrews, M.1
  • 62
    • 0000011289 scopus 로고    scopus 로고
    • Fractional wave-function revivals in the infinite square well
    • D. L. Aronstein and C. R. Stroud, Jr., "Fractional wave-function revivals in the infinite square well," Phys. Rev. A 55, 4526-4537 (1997).
    • (1997) Phys. Rev. A , vol.55 , pp. 4526-4537
    • Aronstein, D.L.1    Stroud Jr., C.R.2
  • 63
    • 4244045533 scopus 로고
    • Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics
    • I. Sh. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 39, 449-453 (1989); "Fractional revivals of wave packets," Acta Phys. Pol. A 78, 33-40 (1990). This paper includes much of the material in the first citation, correcting some minor typographical errors; "Fractional regenerations of wave-packets in the course of long-term evolution of highly excited quantum-systems," Sov. Phys. JETP 69, 464-469 (1989).
    • (1989) Phys. Lett. A , vol.39 , pp. 449-453
    • Averbukh, I.S.1    Perelman, N.F.2
  • 64
    • 4244045533 scopus 로고
    • Fractional revivals of wave packets
    • I. Sh. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 39, 449-453 (1989); "Fractional revivals of wave packets," Acta Phys. Pol. A 78, 33-40 (1990). This paper includes much of the material in the first citation, correcting some minor typographical errors; "Fractional regenerations of wave-packets in the course of long-term evolution of highly excited quantum-systems," Sov. Phys. JETP 69, 464-469 (1989).
    • (1990) Acta Phys. Pol. A , vol.78 , pp. 33-40
  • 65
    • 4244045533 scopus 로고
    • Fractional regenerations of wave-packets in the course of long-term evolution of highly excited quantum-systems
    • I. Sh. Averbukh and N. F. Perelman, "Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 39, 449-453 (1989); "Fractional revivals of wave packets," Acta Phys. Pol. A 78, 33-40 (1990). This paper includes much of the material in the first citation, correcting some minor typographical errors; "Fractional regenerations of wave-packets in the course of long-term evolution of highly excited quantum-systems," Sov. Phys. JETP 69, 464-469 (1989).
    • (1989) Sov. Phys. JETP , vol.69 , pp. 464-469
  • 66
    • 0347107298 scopus 로고    scopus 로고
    • Comparing classical and quantum probability distributions for an asymmetric well
    • M. A. Doncheski and R. W. Robinett, "Comparing classical and quantum probability distributions for an asymmetric well," Eur. J. Phys. 21, 217-228 (2000).
    • (2000) Eur. J. Phys. , vol.21 , pp. 217-228
    • Doncheski, M.A.1    Robinett, R.W.2
  • 67
    • 0000012651 scopus 로고    scopus 로고
    • Femtosecond infrared emission resulting from coherent charge oscillations in quantum wells
    • A. Bonvalet, J. Nagle, V. Berger, A. Migus, J.-L. Martin, and M. Joffre, "Femtosecond infrared emission resulting from coherent charge oscillations in quantum wells," Phys. Rev. Lett. 76, 4392-4395 (1996).
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 4392-4395
    • Bonvalet, A.1    Nagle, J.2    Berger, V.3    Migus, A.4    Martin, J.-L.5    Joffre, M.6


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