Skip to main content
Springer Nature Link
Log in

Coherent States and Their Generalizations for a Charged Particle in a Magnetic Field

  • Conference paper
  • First Online:
Coherent States and Their Applications

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 205))

Abstract

This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
eBook
USD 149.00
Price excludes VAT (USA)
Softcover Book
USD 199.99
Price excludes VAT (USA)
Hardcover Book
USD 199.99
Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Fock, Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld. Z. Phys. 47, 446–448 (1928)

    Article  ADS  MATH  Google Scholar 

  2. C.G. Darwin, The diamagnetism of the free electron. Math. Proc. Cambridge Phil. Soc. 27, 86–90 (1931)

    Article  ADS  MATH  Google Scholar 

  3. L. Page, Deflection of electrons by a magnetic field on the wave mechanics. Phys. Rev. 36, 444–456 (1930)

    Article  ADS  MATH  Google Scholar 

  4. L. Landau, Diamagnetismus der Metalle. Z. Phys. 64, 629–637 (1930)

    Article  ADS  MATH  Google Scholar 

  5. C.G. Darwin, Free motion in wave mechanics. Proc. R. Soc. Lond. A 117, 258–293 (1927)

    Article  ADS  MATH  Google Scholar 

  6. E.H. Kennard, Zur quantenmechanik einfacher bewegungstypen. Z. Phys. 44, 326–352 (1927)

    Article  ADS  MATH  Google Scholar 

  7. K. Husimi, Miscellanea in elementary quantum mechanics I. Prog. Theor. Phys. 9, 238–244 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. M.H. Johnson, B.A. Lippmann, Motion in a constant magnetic field. Phys. Rev. 76, 828–832 (1949)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. I.A. Malkin, V.I. Man’ko, Coherent states of a charged particle in a magnetic field. Zh. Eksp. Teor. Fiz 55, 1014–1025 (1968) [English translation: Sov. Phys. JETP 28, 527–532 (1969)]

    Google Scholar 

  10. R.J. Glauber, Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. J.R. Klauder, Continuous representation theory. II. Generalized relation between quantum and classical dynamics. J. Math. Phys. 4, 1058–1073 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. A.M. Perelomov, Coherent states for arbitrary Lie group. Commun. Math. Phys. 26, 222–236 (1972)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. D.F. Walls, Squeezed states of light. Nature 306, 141–146 (1983)

    Article  ADS  Google Scholar 

  14. K.O. Friedrichs, Mathematical Aspects of the Quantum Theory of Fields (Interscience, New York, 1953)

    MATH  Google Scholar 

  15. L. Infeld, J. Plebański, On a certain class of unitary transformations. Acta Phys. Polon. 14, 41–75 (1955)

    MathSciNet  MATH  Google Scholar 

  16. J. Plebański, Classical properties of oscillator wave packets. Bull. Acad. Pol. Sci. 2, 213–217 (1954)

    MATH  Google Scholar 

  17. A.O. Barut, L. Girardello, New “coherent” states associated with noncompact groups. Commun. Math. Phys. 21, 41–55 (1971)

    Article  ADS  MATH  Google Scholar 

  18. V.V. Dodonov, I.A. Malkin, V.I. Manko, Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597–615 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  19. J.E. Avron, I.W. Herbst, B. Simon, Separaltion of center of mass in homogeneous magnetic fields. Ann. Phys. (NY) 114, 431–451 (1978)

    Article  ADS  MATH  Google Scholar 

  20. B.R. Johnson, J.O. Hirschfelder, K.-H. Yang, Interaction of atoms, molecules, and ions with constant electric and magnetic fields. Rev. Mod. Phys. 55, 109–153 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  21. R. von Baltz, Guiding center motion of two interacting \(n = 0\) Landau electrons in two dimensions. Phys. Lett. A 105, 371–373 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  22. B. Mielnik, A. Ramírez, Magnetic operations: a little fuzzy mechanics? Phys. Scr. 84, 045008 (2011)

    Article  ADS  MATH  Google Scholar 

  23. K. Kowalski, J. Rembieliński, Coherent states of a charged particle in a uniform magnetic field. J. Phys. A Math. Gen. 38, 8247–8258 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. V.V. Dodonov, V.I. Man’ko, Invariants and the evolution of nonstationary quantum systems, in Proceedings of the P.N. Lebedev Physical Institute, ed. by M.A. Markov, vol. 183, (Nauka, Moscow, 1987). [English translation by Nova Science, Commack, New York (1989)]

    Google Scholar 

  25. V.V. Dodonov, Parametric excitation and generation of nonclassical states in linear media, in Theory of Nonclassical States of Light, ed. by V.V. Dodonov, V.I. Man’ko (Taylor & Francis, London, 2003), pp. 153–218

    Google Scholar 

  26. A. Feldman, A.H. Kahn, Landau diamagnetism from the coherent states of an electron in a uniform magnetic field. Phys. Rev. B 1, 4584–4589 (1970)

    Article  ADS  Google Scholar 

  27. W.G. Tam, Coherent states and the invariance group of a charged particle in a uniform magnetic field. Physica 54, 557–572 (1971)

    Article  ADS  Google Scholar 

  28. V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Coherent states of a charged particle in a time-dependent uniform electromagnetic field of a plane current. Physica 59, 241–256 (1972)

    Article  ADS  Google Scholar 

  29. M.H. Boon, Networks of coherent states for electron in magnetic field. Helv. Phys. Acta 48, 551–553 (1975)

    Google Scholar 

  30. S. Varró, Coherent states of an electron in a homogeneous constant magnetic field and the zero magnetic field limit. J. Phys. A Math. Gen. 17, 1631–1638 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  31. E.G.P. Rowe, Classical limit of quantum mechanics (electron in a magnetic field). Am. J. Phys. 59, 1111–1117 (1991)

    Article  ADS  Google Scholar 

  32. J.L. de Melo, I.A. Pedrosa, C. Furtado, Coherent states of Landau-Aharonov-Casher levels. Int. J. Mod. Phys. B 30, 1650022 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Y.I. Granovskii, Y.A. Dimashko, Coherent representation of Green’s functions and magnetism of free electrons. Ukr. Fiz. Zh. 19, 1456–1459 (1974)

    Google Scholar 

  34. E.V. Ivanova, I.A. Malkin, V.I. Manko, Coherent states and radiation of a charged particle in stationary crossed fields. Yadernaya Fizika 21, 664–670 (1975). [English translation: Sov. J. Nucl. Phys. 21, 343–346 (1975)]

    Google Scholar 

  35. D.F. Walls, Quantum statistics of the cyclotron resonance infrared detector. J. Phys. A Math. Gen. 8, 751–758 (1975)

    Article  ADS  Google Scholar 

  36. A.A. Bobrov, O.F. Dorofeev, G.A. Chizhov, Synchrotron radiation of an electron in a coherent state. Teor. Mat. Fiz. 61, 293–300 (1984). [English translation: Theor. Math. Phys. 61, 1149–1154 (1984)]

    Article  ADS  Google Scholar 

  37. R.G. Agayeva, Fluctuation of thermomagnetic current. J. Phys. C Solid State Phys. 18, 5841–5848 (1985)

    Article  ADS  Google Scholar 

  38. S.T. Pavlov, A.V. Prokhorov, Density of electron states in metals and coherent states. Fiz. Tverd. Tela 32, 3451–3453 (1990) [English translation: Sov. Phys. Solid State 32, 2001–2002 (1990)]

    Google Scholar 

  39. S.T. Pavlov, A.V. Prokhorov, Oscillation effects in metals in a magnetic field and macroscopic quantum interference. Zh. Eksp. Teor. Fiz. 100, 510–519 (1991). [English translation: Sov. Phys. JETP 73, 280–285 (1991)]

    Google Scholar 

  40. S.T. Pavlov, I.S. Pivovarov, Dingle factor in the de Haas-van Alphen effect and the method of coherent states. Fiz. Tverd. Tela 33, 1615–1618 (1991)

    Google Scholar 

  41. A. Jellal, Orbital magnetism of a two-dimensional noncommutative confined system. J. Phys. A Math. Gen. 34, 10159–10177 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. G. Cristofano, D. Giuliano, G. Maiella, L. Valente, 2D electron in an external magnetic field in the presence of dissipation. Int. J. Mod. Phys. B 9, 707–718 (1995)

    Article  ADS  Google Scholar 

  43. G. Cristofano, D. Giuliano, G. Maiella, 2D electron in a magnetic field with dissipation. J. Phys. I France 6, 861–872 (1996)

    Article  ADS  Google Scholar 

  44. D. Schuch, M. Moshinsky, Coherent states and dissipation for the motion of a charged particle in a constant magnetic field. J. Phys. A Math. Gen. 36, 6571–6585 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  45. F.T. Hadjioannou, N.V. Sarlis, Coherent states for the two-dimensional magnetic-electric Euclidean group MEE(2). Phys. Rev. B 56, 9406–9413 (1997)

    Article  ADS  Google Scholar 

  46. S.T. Ali, F. Bagarello, Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians. J. Math. Phys. 46, 053518 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. S.T. Ali, F. Bagarello, G. Honnouvo, Modular structures on trace class operators and applications to Landau levels. J. Phys. A Math. Theor. 43, 105202 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. E. Drigho-Filho, S. Kuru, J. Negro, L.M. Nieto, Superintegrability of the Fock-Darwin system. Ann. Phys. 383, 101–119 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. H.R. Lewis Jr., W.B. Riesenfeld, An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10, 1458–1473 (1969)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Invariants and evolution of coherent states for charged particle in time-dependent magnetic field. Phys. Lett. A 30, 414–416 (1969)

    Article  ADS  Google Scholar 

  51. Malkin, I.A., Man’ko, V.I., Trifonov, D.A.: Evolution of coherent states of a charged particle in a variable magnetic field. Zh. Eksp. Teor. Fiz. 58, 721–729 (1970) [English translation: Sov. Phys. JETP 31, 386–390 (1970)]

    Google Scholar 

  52. I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Coherent states and transition probabilities in a time-dependent electromagnetic field. Phys. Rev. D 2, 1371–1385 (1970)

    Article  ADS  Google Scholar 

  53. I.A. Malkin, V.I. Man’ko, Coherent states and Green’s function of a charged particle in variable electric and magnetic fields. Zh. Eksp. Teor. Fiz. 59, 1746–1754 (1970). [English translation: Sov. Phys. JETP 32, 949–953 (1971)]

    Google Scholar 

  54. A. Holz, \(N\)-dimensional anisotropic oscillator in a uniform time-dependent electromagnetic field. Lett. Nuovo Cim. 4, 1319–1323 (1970)

    Article  Google Scholar 

  55. I.A. Malkin, V.I. Man’ko, D.A. Trifonov, Linear adiabatic invariants and coherent states. J. Math. Phys. 14, 576–582 (1973)

    Article  ADS  Google Scholar 

  56. V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Integrals of the motion, Green functions and coherent states of dynamical systems. Int. J. Theor. Phys. 14, 37–54 (1975)

    Article  MathSciNet  Google Scholar 

  57. M.S. Abdalla, Charged harmonic oscillator in the presence of electric and magnetic fields. Nuovo Cim. B 101, 267–283 (1988)

    Article  ADS  Google Scholar 

  58. I.A. Malkin, V.I. Man’ko, Coherent states and excitation of a charged particle in a constant magnetic field by means of an electric field. Teor. Mat. Fiz. 6, 71–77 (1971). [English translation: Theor. Math. Phys. 6, 51–55 (1971)]

    Article  ADS  Google Scholar 

  59. R.G. Agayeva, Non-adiabatic parametric excitation of oscillator-type systems. J. Phys. A Math. Gen. 13, 1685–1699 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  60. G. Fiore, L. Gouba, Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field. J. Math. Phys. 52, 103509 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. V.G. Bagrov, V.V. Belov, I.M. Ternov, Quasiclassical trajectory-coherent states of a particle in an arbitrary electromagnetic field. J. Math. Phys. 24, 2855–2859 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  62. V.V. Dodonov, V.I. Man’ko, D.L. Ossipov, Quantum evolution of the localized states. Phys. A 168, 1055–1072 (1990)

    Article  Google Scholar 

  63. V.V. Belov, D.V. Boltovskii, A.G. Karavayev, Quasi-classical trajectory-coherent states of a nonrelativistic particle in a uniform magnetic-field. Izv. Vyssh. Uchebn. Zaved. Fiz. 6, 113–117 (1990)

    Google Scholar 

  64. M. Mǎntoiu, R. Purice, S. Richard, Coherent states and pure state quantization in the presence of a variable magnetic field. Int. J. Geom. Meth. Mod. Phys. 8, 187–202 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  65. S. Ryu, M. Kataoka, H.S. Sim, Ultrafast emission and detection of a single-electron Gaussian wave packet: a theoretical study. Phys. Rev. Lett. 117, 146802 (2016)

    Article  ADS  Google Scholar 

  66. I.I. Rabi, Das freie Elektron im homogenen magnetfeld nach der Diracschen theorie. Z. Phys. 49, 507–511 (1928)

    Article  ADS  MATH  Google Scholar 

  67. V.G. Bagrov, I.L. Bukhbinder, D.M. Gitman, Coherent states of relativistic particles. Izv. Vyssh. Uchebn. Zaved. Fiz., 8, 135–136 (1975). [English translation: Sov. Phys. J. 18, 1180–1181 (1975)]

    Google Scholar 

  68. V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Coherent states and Green functions of relativistic quadratic systems. Physica A 82, 113–133 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  69. V.G. Bagrov, I.L. Buchbinder, D.M. Gitman, Coherent states of a relativistic particle in an external electromagnetic field. J. Phys. A Math. Gen. 9, 1955–1965 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  70. I.M. Ternov, V.G. Bagrov, On coherent states of relativistic particles. Ann. Physik 40, 2–9 (1983)

    MathSciNet  Google Scholar 

  71. E. Colavita, S. Hacyan, Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field. Ann. Phys. (NY) 342, 205–213 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  72. G.M. Filippov, Interaction of radiation and a relativistic electron in motion in a constant magnetic field. Zh. Eksp. Teor. Fiz. 113, 841–864 (1998). [English translation: Sov. Phys. JETP 86, 459–471 (1998)]

    Google Scholar 

  73. V.G. Bagrov, V.V. Belov, Quasiclassical coherent trajectory states of a spinless relativistic particle in an arbitrary electromagnetic field. Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 48–50 (1982). [English translation: Sov. Phys. J. 25, 333–335 (1982)]

    Google Scholar 

  74. V.V. Belov, A.G. Karavayev, Quasi-classical trajectory-coherent states of relativistic spinless particle in a homogeneous magnetic field. Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 110–112 (1988)

    Google Scholar 

  75. L.V. Gritsenko, I.P. Susak, A.Y. Trifonov, Trajectory-coherent states for the Klein–Gordon equation in its \(\Phi \)-representation. Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 44–49 (1999) [English translation: Russ. Phys. J. 42, 897–901 (1999)]

    Google Scholar 

  76. V.G. Bagrov, V.V. Belov, A.Y. Trifonov, Theory of spontaneous radiation by electrons in a trajectory-coherent approximation. J. Phys. A Math. Gen. 26, 6431–6449 (1993)

    Article  ADS  Google Scholar 

  77. A. Mostafazadeh, F. Zamani, Quantum mechanics of Klein-Gordon fields II: relativistic coherent states. Ann. Phys. (NY) 321, 2210–2241 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  78. A. Bermudez, M.A. Martin-Delgado, E. Solano, Mesoscopic superposition states in relativistic Landau levels. Phys. Rev. Lett. 99, 123602 (2007)

    Google Scholar 

  79. V.Y. Demikhovskii, G.M. Maksimova, A.A. Perov, A.V. Telezhnikov, Long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival. Phys. Rev. A 85, 022105 (2012)

    Article  ADS  Google Scholar 

  80. H.Y. Kim, J.H. Weiner, Gaussian-wave-packet dynamics in uniform magnetic and quadratic potential fields. Phys. Rev. B 7, 1353–1362 (1973)

    Article  ADS  Google Scholar 

  81. A. Bechler, Generation of squeezed states in a homogeneous magnetic field. Phys. Lett. A 130, 481–482 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  82. A. Jannussis, E. Vlahos, D. Skaltsas, G. Kliros, V. Bartzis, Squeezed states in the presence of a time-dependent magnetic field. Nuovo Cim. B 104, 53–66 (1989)

    Article  ADS  Google Scholar 

  83. M.S. Abdalla, Statistical properties of a charged oscillator in the presence of a constant magnetic field. Phys. Rev. A 44, 2040–2047 (1991)

    Article  ADS  Google Scholar 

  84. V.A. Kovarskiy, Coherent and squeezed states of Landau oscillators in a solid. Emission of nonclassical light. Fiz. Tverd. Tela 34, 3549–3553 (1992) [English translation: Sov. Phys. - Solid State 34, 1900–1902 (1992)]

    Google Scholar 

  85. B. Baseia, On the generation of squeezing for a charged oscillator in a magnetic field. Phys. Lett. A 170, 311–314 (1992)

    Article  ADS  Google Scholar 

  86. B. Baseia, S.S. Mizrahi, M.H.Y. Moussa, Generation of squeezing for a charged oscillator and a charged particle in a time dependent electromagnetic field. Phys. Rev. A 46, 5885–5889 (1992)

    Article  ADS  Google Scholar 

  87. F.C. Delgado, B. Mielnik, Magnetic control of squeezing effects. J. Phys. A Math. Gen. 31, 309–320 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  88. J.E. Santos, N.M.R. Peres, J.M.B. Lopes dos Santos, Evolution of squeezed states under the Fock-Darwin Hamiltonian. Phys. Rev. A 80, 053401 (2009)

    Article  ADS  Google Scholar 

  89. V.V. Dodonov, E.V. Kurmyshev, V.I. Man’ko, Correlated coherent states, in Classical And Quantum Effects In Electrodynamics, Proceedings of the P.N. Lebedev Physical Institute, ed. by A.A. Komar, vol. 176 (Nauka, Moscow, 1986), pp. 128–150 [English translation by Nova Science, Commack, New York (1988), pp. 169–199]

    Google Scholar 

  90. A. Dehghani, H. Fakhri, B. Mojaveri, The minimum-uncertainty coherent states for Landau levels. J. Math. Phys. 53, 123527 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  91. C. Aragone, New squeezed Landau states. Phys. Lett. A 175, 377–381 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  92. V.V. Dodonov, V.I. Man’ko, P.G. Polynkin, Geometrical squeezed states of a charged particle in a time-dependent magnetic field. Phys. Lett. A 188, 232–238 (1994)

    Article  ADS  Google Scholar 

  93. M. Ozana, A.L. Shelankov, Squeezed states of a particle in magnetic field. Fiz. Tverd. Tela 40, 1405–1412 (1998). [English translation: Phys. Solid State 40, 1276–1282 (1998)]

    Article  ADS  Google Scholar 

  94. A.B. Dzyubenko, Charged two-dimensional magnetoexciton and two-mode squeezed vacuum states. Pis’ma v Zh. Eksp. Teor. Fiz. 74, 352–356 (2001). [English translation: JETP Lett. 74, 318–322 (2001)]

    Article  ADS  Google Scholar 

  95. A.B. Dzyubenko, Charged hydrogenic problem in a magnetic field: Noncommutative translations, unitary transformations, and coherent states. Phys. Rev. B 65, 035318 (2001)

    Article  ADS  Google Scholar 

  96. H. Takahasi, Information theory of quantum mechanical channels, in Advances in Communication Systems, vol. l, Theory and Applications, ed. by A.V. Balakrishnan (Academic Press, New York, 1965), pp. 227–310

    Google Scholar 

  97. V.V. Dodonov, Man’ko, V.I.: Correlated and squeezed coherent states of time-dependent quantum systems, in Advances in Chemical Physics Modern Nonlinear Optics, eds. by M. Evans, S. Kielich, vol. LXXXV, part 3. (Wiley, New York, 1994), pp. 499–530

    Google Scholar 

  98. A. Lukš, V. Peřinová, Z. Hradil, Principal squeezing. Acta Phys. Polon. A 74, 713–721 (1988)

    Google Scholar 

  99. V.V. Dodonov, “Nonclassical” states in quantum optics: a “squeezed” review of the first 75 years. J. Opt. B Quantum Semiclass. Opt. 4, R1–R33 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  100. V.V. Dodonov, Universal integrals of motion and universal invariants of quantum systems. J. Phys. A Math. Gen. 33, 7721–7738 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  101. V.V. Dodonov, V.I. Man’ko, Density matrices and Wigner functions of quasiclassical quantum systems, in Group Theory, Gravitation and Elementary Particle Physics, Proceedings of the P.N. Lebedev Physical Institute, ed. by A.A. Komar, vol. 167(Nauka, Moscow, 1986), pp. 7–79. [English translation by Nova Science, Commack, New York (1987), pp. 7–101]

    Google Scholar 

  102. L.D. Landau, E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1969)

    MATH  Google Scholar 

  103. V.V. Dodonov, A.B. Klimov, D.E. Nikonov, Quantum phenomena in nonstationary media. Phys. Rev. A 47, 4422–4429 (1993)

    Article  ADS  MATH  Google Scholar 

  104. P. Gulshani, A.B. Volkov, Heisenberg-symplectic angular-momentum coherent states in two dimensions. J. Phys. A Math. Gen. 13, 3195–3204 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  105. P. Gulshani, A.B. Volkov, The cranked oscillator coherent states. J. Phys. G Nucl. Phys. 6, 1335–46 (1980)

    Article  ADS  Google Scholar 

  106. S. Hacyan, Squeezed states and uncertainty relations in rotating frames and Penning trap. Phys. Rev. A 53, 4481–4487 (1996)

    Article  ADS  Google Scholar 

  107. A. Wünsche, The quantum-mechanical inhomogeneous symplectic group. J. Opt. B Quantum Semiclass. Opt. 4, 1–14 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  108. C. Bracher, Uncertainty relations for angular momentum eigenstates in two and three spatial dimensions. Am. J. Phys. 79, 313–319 (2011)

    Article  ADS  Google Scholar 

  109. L. Rebón, R. Rossignoli, Entanglement of two harmonic modes coupled by angular momentum. Phys. Rev. A 84, 052320 (2011)

    Article  ADS  Google Scholar 

  110. L. Rebón, N. Canosa, R. Rossignoli, Dynamics of entanglement between two harmonic modes in stable and unstable regimes. Phys. Rev. A 89, 042312 (2014)

    Article  ADS  Google Scholar 

  111. D.V. Karlovets, Gaussian and Airy wave packets of massive particles with orbital angular momentum. Phys. Rev. A 91, 013847 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  112. V.V. Dodonov, Rotating quantum Gaussian packets. J. Phys. A Math. Theor. 48, 435303 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  113. V.V. Dodonov, Rotating highly mixed Gaussian packets with minimal energy. Phys. Rev. A 93, 022106 (2016)

    Article  ADS  Google Scholar 

  114. A. Goussev, Rotating Gaussian wave packets in weak external potentials. Phys. Rev. A 96, 013617 (2017)

    Article  ADS  Google Scholar 

  115. G. Loyola, M. Moshinsky, A. Szczepaniak, Coherent states and accidental degeneracy for a charged particle in a magnetic field. Am. J. Phys. 57, 811–814 (1989)

    Article  ADS  Google Scholar 

  116. R. Ferrari, Two-dimensional electrons in a strong magnetic field: a basis for single-particle states. Phys. Rev. B 42, 4598–4609 (1990)

    Article  ADS  Google Scholar 

  117. Z. Mouayn, Characterization of two-dimensional Euclidean Landau states by coherent state transforms. J. Phys. A Math. Gen. 37, 4813–4819 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  118. W.-L. Yang, J.-L. Chen, Berry’s phase for coherent states of Landau levels. Phys. Rev. A 75, 024101 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  119. M.N. Rhimi, R. El-Bahi, Geometric phases for wave packets of the Landau problem. Int. J. Theor. Phys. 47, 1095–1111 (2008)

    Article  MATH  Google Scholar 

  120. L.D. Abreu, P. Balazs, M. de Gosson, Z. Mouayn, Discrete coherent states for higher Landau levels. Ann. Phys. (NY) 363, 337–353 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  121. H.-Y. Fan, H. Zou, Y. Fan, Angular momentum conserved coherent state for an electron in a uniform magnetic field. Chin. Phys. Lett. 16, 706–708 (1999)

    Article  ADS  Google Scholar 

  122. D. Bhaumik, K. Bhaumik, B. Dutta-Roy, Charged bosons and the coherent state. J. Phys. A Math. Gen. 9, 1507–1512 (1976)

    Article  ADS  Google Scholar 

  123. H. Fakhri, \(su(1, 1)\)-Barut-Girardello coherent states for Landau levels. J. Phys. A Math. Gen. 37, 5203–5210 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  124. I. Aremua, M.N. Hounkonnou, E. Baloïtcha, Coherent states for Landau levels: algebraic and thermodynamical properties. Rep. Math. Phys. 76, 247–269 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  125. A. Dehghani, B. Mojaveri, Generalized su(2) coherent states for the Landau levels and their nonclassical properties. Eur. Phys. J. D 67, 264 (2013)

    Article  ADS  Google Scholar 

  126. M. Novaes, J.P. Gazeau, Multidimensional generalized coherent states. J. Phys. A Math. Gen. 36, 199–212 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  127. H. Fakhri, Generalized Klauder-Perelomov and Gazeau-Klauder coherent states for Landau levels. Phys. Lett. A 313, 243–251 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  128. M.R. Setare, A. Fallahpour, Generalized coherent states for charged particle in uniform and variable magnetic field. Acta Phys. Polon. B 40, 217–228 (2009)

    ADS  Google Scholar 

  129. P.M. Mathews, K. Eswaran, Semi-coherent states of the quantum harmonic oscillator. Nuovo Cim. B 17, 332–335 (1973)

    Article  ADS  Google Scholar 

  130. V.V. Dodonov, M.B. Renó, Nonclassical properties of “semi-coherent” quantum states. J. Phys. A Math. Gen. 39, 7411–7422 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  131. A. Dehghani, B. Mojaveri, New semi coherent states: nonclassical properties. Int. J. Theor. Phys. 54, 3507–3515 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  132. R.L. Matos Filho, W. Vogel, Nonlinear coherent states. Phys. Rev. A 54, 4560–4563 (1996)

    Article  ADS  Google Scholar 

  133. V.I. Man’ko, G. Marmo, E.C.G. Sudarshan, F. Zaccaria, f-oscillators and nonlinear coherent states. Phys. Scr. 55, 528–541 (1997)

    Article  ADS  Google Scholar 

  134. S. Sivakumar, Studies on nonlinear coherent states. J. Opt. B Quantum. Semiclass Opt. 2, R61–R75 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  135. J.P. Gazeau, J.R. Klauder, Coherent states for systems with discrete and continuous spectrum. J. Phys. A Math. Gen. 32, 123–132 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  136. D. Herrera, A.M. Valencia, F. Pennini, S. Curilef, A charged particle in a magnetic field: a review of two formalisms of coherent states and the Husimi function. Eur. J. Phys. 29, 439–449 (2008)

    Article  MATH  Google Scholar 

  137. J.P. Gazeau, M.C. Baldiotti, D.M. Gitman, Coherent states of a particle in a magnetic field and the Stieltjes moment problem. Phys. Lett. A 373, 1916–1920 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  138. B.I. Lev, A.A. Semenov, C.V. Usenko, Behaviour of \(\pi ^{\pm }\) mesons and synchrotron radiation in a strong magnetic field. Phys. Lett. A 230, 261–268 (1997)

    Article  ADS  Google Scholar 

  139. B.I. Lev, A.A. Semenov, C.V. Usenko, J.R. Klauder, Relativistic coherent states and charge structure of the coordinate and momentum operators. Phys. Rev. A 66, 022115 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  140. H. Feshbach, F. Villars, Elementary relativistic wave mechanics of spin 0 and spin 1/2 particles. Rev. Mod. Phys. 30, 24–45 (1958)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  141. H.-Y. Fan, Y. Fan, Angular momentum-phase coherent state for an electron in uniform magnetic field. Chin. Phys. Lett. 18, 319–321 (2001)

    Article  ADS  Google Scholar 

  142. G.S. Agarwal, K. Tara, Nonclassical properties of states generated by the excitations of a coherent state. Phys. Rev. A 43, 492–497 (1991)

    Article  ADS  Google Scholar 

  143. B. Mojaveri, A. Dehghani, Generation of excited coherent states for a charged particle in a uniform magnetic field. J. Math. Phys. 56, 041704 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  144. V.G. Bagrov, D.M. Gitman, V.D. Skarzhinsky, The Aharonov–Bohm effect for stationary and coherent states of an electron in a uniform magnetic field. in Classical and Quantum Effects in Electrodynamics Proceedings of the P.N. Lebedev Physical Institute, ed. by A.A. Komar, vol. 176. (Nauka, Moscow, 1986), pp. 151–165. [English translation by Nova Science, Commack, New York (1988), pp. 201–219]

    Google Scholar 

  145. V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, D.P. Meira Filho, Coherent states of non-relativistic electron in the magneticsolenoid field. J. Phys. A Math. Theor. 43, 354016 (2010)

    Article  MATH  Google Scholar 

  146. V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, D.P. Meira Filho, Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid. J. Phys. A Math. Theor. 44, 055301 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  147. V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, K. Gorska, Completeness for coherent states in a magnetic-solenoid field. J. Phys. A Math. Theor. 45, 244008 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  148. V.V. Belov, M.F. Kondrat’eva, The Aharonov–Bohm effect for nonstationary quasiclassical trajectory-coherent states in a uniform magnetic field. Izv. Vyssh. Uchebn. Zaved., Fiz. 10, 83–90 (1992). [English translation: Russ. Phys. J. 35, 961–968 (1993)]

    Google Scholar 

  149. H. Fakhri, B. Mojaveri, M.A. Gomshi Nobary, Landau levels as a limiting case of a model with the Morse-like magnetic field. Rep. Math. Phys. 66, 299–310 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  150. B. Mojaveri, Klauder-Perelomov and Gazeau-Klauder coherent states for an electron in the Morse-like magnetic field. Eur. Phys. J. D 67, 105 (2013)

    Article  ADS  Google Scholar 

  151. J. Beckers, D. Dehin, V. Hussin, Dynamical and kinematical supersymmetries of the quantum harmonic oscillator and the motion in a constant magnetic field. J. Phys. A Math. Gen. 21, 651–667 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  152. B.W. Fatyga, V.A. Kostelecký, M.M. Nieto, D.R. Truax, Supercoherent states. Phys. Rev. D 43, 1403–1412 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  153. H. Fakhri, H. Motavali, Parasupersymmetric coherent states for Landau levels with dynamical symmetry group \(H_4\). Int. J. Mod. Phys. A 17, 4081–4093 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  154. S.T. Ali, F. Bagarello, Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry. J. Math. Phys. 49, 032110 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  155. V.A. Kostelecký, V.I. Man’ko, M.M. Nieto, D.R. Truax, Supersymmetry and a time-dependent Landau system. Phys. Rev. A 48, 951–963 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  156. M.C. Baldiotti, J.P. Gazeau, D.M. Gitman, Semiclassical and quantum motions on the non-commutative plane. Phys. Lett. A 373, 3937–3943 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  157. M.-L. Liang, Y. Jiang, Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane. Phys. Lett. A 375, 1–5 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  158. Z. Mouayn, Coherent states attached to Landau levels on the Poincare disc. J. Phys. A Math. Gen. 38, 9309–9316 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  159. Z. Mouayn, Coherent states attached to Landau levels on the Riemann sphere. Rep. Math. Phys. 55, 269–276 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  160. B.C. Hall, J.J. Mitchell, Coherent states for a 2-sphere with a magnetic field. J. Phys. A Math. Theor. 45, 244025 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  161. Y. Kurochkin, I. Rybak, D. Shoukavy, Coherent states on horospheric three-dimensional Lobachevsky space. J. Math. Phys. 57, 082111 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  162. M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime. Ann. Phys. (NY) 372, 283–296 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

I thank Prof. J.-P. Antoine and Prof. J.-P. Gazeau for inviting me to the conference “Coherent states and their applications: A contemporary panorama”, and for the patience, waiting for this contribution. I am grateful to CIRM–Marseille for covering my local expenses. A partial support of the Brazilian agency CNPq is acknowledged.

Author information

Authors and Affiliations

  1. Institute of Physics and International Center for Physics, University of Brasilia, Brasilia, Brazil

    Viktor V. Dodonov

Authors
  1. Viktor V. Dodonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Viktor V. Dodonov .

Editor information

Editors and Affiliations

  1. Institut de recherche en mathématique et physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  2. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Palermo, Italy

    Fabio Bagarello

  3. Laboratoire APC, Paris Diderot University, Paris, France

    Jean-Pierre Gazeau

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dodonov, V.V. (2018). Coherent States and Their Generalizations for a Charged Particle in a Magnetic Field. In: Antoine, JP., Bagarello, F., Gazeau, JP. (eds) Coherent States and Their Applications. Springer Proceedings in Physics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-76732-1_15

Download citation

Publish with us

Policies and ethics

Search

Navigation