Skip to main content
SpringerLink
Log in

Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

  • Chapter
  • First Online:
Integrability, Supersymmetry and Coherent States

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

A short review of the main properties of coherent and squeezed states is given in the introductory form. The efforts are addressed to clarify concepts and notions, including some passages of the history of science, with the aim of facilitating the subject for nonspecialists. In this sense, the present work is intended to be complementary to other papers of the same nature and subject in current circulation.

To Prof. Veronique Hussin on his 60th birthday with friendship and scientific admiration.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L. Mandel, E. Wolf, Coherence properties of optical fields. Rev. Mod. Phys. 37, 231 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  2. R.H. Brown, R.Q. Twiss, Correlation between photons in two coherent beams of light. Nature 177, 27 (1956)

    Article  ADS  Google Scholar 

  3. R.H. Brown, R.Q. Twiss, Interferometry of the intensity fluctuations in light I. Basic theory: the correlation between photons in coherent beams of radiation. Proc. R. Soc. Lond. A242, 300 (1957)

    MATH  Google Scholar 

  4. R.H. Brown, R.Q. Twiss, Interferometry of the intensity fluctuations in light II. An experimental test of the theory for partially coherent light. Proc. R. Soc. Lond. A243, 291 (1958)

    Google Scholar 

  5. G.J. Troup, R.G. Turner, Optical coherence theory. Rep. Prog. Phys. 37, 771 (1974)

    Article  ADS  Google Scholar 

  6. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995)

    Book  Google Scholar 

  7. M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999)

    Book  Google Scholar 

  8. R.J. Glauber, Photon correlations. Phys. Rev. Lett. 10, 84 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  9. R.J. Glauber, The quantum theory of optical coherence. Phys. Rev. 130, 2529 (1963)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. D.F. Walls, Evidence for the quantum nature of light. Nature 280, 451 (1979)

    Article  ADS  Google Scholar 

  12. R.J. Glauber, Optical coherence and photon statistics, in Quantum Optics and Electronics, ed. by C. DeWitt, A. Blandin, C. Cohen-Tannoudji (Gordon and Breach, New York, 1964), pp. 65–185

    Google Scholar 

  13. R.J. Glauber, Quantum Theory of Optical Coherence. Selected Papers and Lectures (Wiley-VCH, Weinheim, 2007)

    Google Scholar 

  14. P. Grangier, G. Roger, A. Aspect, Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. Europhys. Lett. 1, 173 (1986)

    Article  ADS  Google Scholar 

  15. W. Rueckner, J. Peidle, Young’s double-slit experiment with single photons and quantum eraser. Am. J. Phys. 81, 951 (2013)

    Article  ADS  Google Scholar 

  16. R.S. Aspden, M.J. Padgett, G.C. Spalding, Video recording true single-photon double-slit interference. Am. J. Phys. 84, 671 (2016)

    Article  ADS  Google Scholar 

  17. J.R. Klauder, The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers. Ann. Phys. 11, 123 (1960)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. E.C.G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. H. Takahasi, Information theory of quantum-mechanical channels. Adv. Commun. Syst. 1, 227 (1965)

    Article  Google Scholar 

  20. D.R. Robinson, The ground state of the Bose gas. Commun. Math. Phys. 1, 159 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  21. D. Stoler, Equivalence classes of minimum uncertainty packets. Phys. Rev. D 1, 3217 (1970)

    Article  ADS  Google Scholar 

  22. D. Stoler, Equivalence classes of minimum uncertainty packets II. Phys. Rev. D 4, 1925 (1971)

    Article  ADS  Google Scholar 

  23. E.Y.C. Lu, New coherent states of the electromagnetic field. Lett. Nuovo Cimento 2, 1241 (1971)

    Article  Google Scholar 

  24. E.Y.C. Lu, Quantum correlations in two-photon amplification. Lett. Nuovo Cimento 2, 585 (1972)

    Article  Google Scholar 

  25. H.P. Yuen, Two-photon coherent states of the radiation field. Phys. Rev. A 13, 2226 (1976)

    Article  ADS  Google Scholar 

  26. V.V. Dodonov, E.V. Kurmyshev, V.I. Man’ko, Generalized uncertainty relation and correlated coherent states. Phys. Lett. A. 79, 150 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  27. A.K. Rajagopal, J.T. Marshall, New coherent states with applications to time-dependent systems. Phys. Rev. A 26, 2977 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  28. H.P. Yuen, Contractive states and the standard quantum limit for monitoring free-mass positions. Phys. Rev. Lett. 51, 719 (1983)

    Article  ADS  Google Scholar 

  29. H.P. Yuen, J.H. Shapiro, Optical communication with two-photon coherent states–Part I: quantum-state propagation and quantum-noise. IEEE Trans. Inf. Theory 24, 657 (1978)

    Article  ADS  MATH  Google Scholar 

  30. J.H. Shapiro, H.P. Yuen, J.A. Machado Mata, Optical communication with two-photon coherent states–Part II: photoemissive detection and structured receiver performance. IEEE Trans. Inf. Theory 25, 179 (1979)

    Article  ADS  MATH  Google Scholar 

  31. H.P. Yuen, J.H. Shapiro, Optical communication with two-photon coherent states–Part III: quantum measurements realizable with photoemissive detectors. IEEE Trans. Inf. Theory 26, 78 (1980)

    Article  ADS  MATH  Google Scholar 

  32. P. Hariharan, Optical Interferometry (Academic Press, San Diego, 2003)

    Google Scholar 

  33. M.P. Silverman, Quantum Superposition. Counterintuitive Consequences of Coherence, Entanglement, and Interference (Springer, Berlin, 2008)

    Google Scholar 

  34. J.N. Hollenhorst, Quantum limits on resonant-mass gravitational-radiation detectors. Phys. Rev. D 19, 1669 (1979)

    Article  ADS  Google Scholar 

  35. V.B. Braginsky, Y.I. Vorontsov, K.S. Thorne, Quantum nondemolition measurements. Science 209, 547 (1980)

    Article  ADS  Google Scholar 

  36. C.M. Caves, Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75 (1980)

    Article  ADS  Google Scholar 

  37. C.M. Caves, K.S. Thorne, R.W.P. Drever, V.D. Sandberg, M. Zimmerman, On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341 (1980)

    ADS  Google Scholar 

  38. K.S. Thorne, Black Holes and Time Warps. Einstein’s Outrageous Legacy (W.W. Norton & Company, New York, 1994)

    Google Scholar 

  39. R. Schnabel, N. Mavalvala, D.E. McClelland, P.K. Lam, Quantum metrology for gravitational wave astronomy. Nat. Commun. 1, 121 (2010)

    Article  ADS  Google Scholar 

  40. P.R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, 2nd edn. (World Scientific, Singapore, 2017)

    Book  MATH  Google Scholar 

  41. D.F. Walls, Squeezed states of light. Nature 306, 141 (1983)

    Article  ADS  Google Scholar 

  42. R. Loudon, P.L. Knight, Squeezed light. J. Mod. Opt. 34, 709 (1987)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. M.C. Teich, B.E.A. Saleh, Squeezed states of light. Quantum Opt. 1, 153 (1989)

    Article  ADS  Google Scholar 

  44. V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  45. C.C. Gerry, Non-classical properties of even and odd coherent states. J. Mod. Opt. 40, 1053 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. R.L. de Matos Filho, W. Vogel, Even and odd coherent states of the motion of a trapped ion. Phys. Rev. Lett. 76, 608 (1996)

    Article  ADS  Google Scholar 

  47. B. Roy, P. Roy, Coherent states, even and odd coherent states in a finite-dimensional Hilbert space and their properties. J. Phys. A Math. Gen. 31, 1307 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. W. Moore, Schrödinger. Life and Tough (Cambridge University Press, Cambridge, 1987)

    Google Scholar 

  49. E.P. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749 (1932)

    Article  ADS  MATH  Google Scholar 

  50. T.L. Curtright, D.B. Fairlie, C.K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space (World Scientific, Singapore, 2014)

    Book  MATH  Google Scholar 

  51. A. Kenfack, K. Zyczkowski, Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B Quantum Semiclass. Opt. 6, 396 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  52. G.H. Agarwal, Quantum Optics (Cambridge University Press, Cambridge, 2013)

    MATH  Google Scholar 

  53. L. Mandel, Sub-Poissonian photon statistics in resonance fluorescence. Opt. Express 4, 205 (1979)

    ADS  Google Scholar 

  54. M.S. Kim, W. Son, V. Buzek, P.L. Knight, Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  55. X.-b. Wang, Theorem for the beam-splitter entangler. Phys. Rev. A 66, 024303 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  56. V.V. Dodonov, V.I. Man’ko (eds.), Theory of Nonclassical States of Light (Taylor and Francis, London, 2003)

    Google Scholar 

  57. D. Bouwmeester, A. Ekert, A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer, New York, 2000)

    Book  MATH  Google Scholar 

  58. L.C. Biedenharn, The quantum group SU q(2) and a q-analogue of the boson operators. J. Phys. A Math. Gen. 22, L873 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. A.J. Macfarlane, On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q. J. Phys. A Math. Gen. 22, 4581 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. A.I. Solomon, A characteristic functional for deformed photon phenomenology. Phys. Lett. A 196, 29 (1994)

    Article  ADS  Google Scholar 

  61. R.L. de Matos Filho, W. Vogel, Nonlinear coherent states. Phys. Rev. A 54, 4560 (1996)

    Article  ADS  Google Scholar 

  62. V.I. Ma’ko, G. Marmo, E.C.G. Sudarshan, F. Zaccaria, f-oscillators and nonlinear coherent states. Phys. Scrip. 55, 528 (1997)

    Google Scholar 

  63. F. Cooper, A. Khare, U. Sukhatme, Supersymmetry and quantum mechanics. Phys. Rep. 251, 267 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. B.K. Bagchi, Supersymmetry in Quantum and Classical Mechanics (Chapman & Hall, Boca Raton, 2001)

    MATH  Google Scholar 

  65. H. Aoyama, M. Sato, T. Tanaka, General forms of a N-fold supersymmetric family. Phys. Lett. B 503, 423 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. H. Aoyama, M. Sato, T. Tanaka, N-fold supersymmetry in quantum mechanics: general formalism. Nucl. Phys. B 619, 105 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  67. B. Mielnik, O. Rosas-Ortiz, Factorization: little or great algorithm? J. Phys. A Math. Gen. 37, 10007 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. A.A. Andrianov, M.V. Ioffe, Nonlinear supersymmetric quantum mechanics: concepts and realizations. J. Phys. A Math. Gen. 45, 503001 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  69. A. Gangopadhyaya, J. Mallow, C. Rasinari, Supersymmetric Quantum Mechanics: An Introduction, 2nd edn. (World Scientific, Singapore, 2018)

    MATH  Google Scholar 

  70. B. Mielnik, Factorization method and new potentials with the oscillator spectrum. J. Math. Phys. 25, 3387 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  71. 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 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  72. V.M. Eleonsky, V.G. Korolev, Isospectral deformation of quantum potentials and the Liouville equation. Phys. Rev. A 55, 2580 (1997)

    Article  ADS  Google Scholar 

  73. S. Seshadri, V. Balakrishnan, S. Lakshmibala, Ladder operators for isospectral oscillators. J. Math. Phys. 39, 838 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. C.L. Williams, N.N. Pandya, B.G. Bodmann, Coupled supersymmetry and ladder structures beyond the harmonic oscillator. Mol. Phys. 116, 2599 (2018)

    Article  ADS  Google Scholar 

  75. Y. Berube-Lauziere, V. Hussin, Comments of the definitions of coherent states for the SUSY harmonic oscillator. J. Phys. A Math. Gen. 26, 6271 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  76. D.J. Fernandez, V. Hussin, L.M. Nieto, Coherent states for isospectral oscillator Hamiltonians. J. Phys. A Math. Gen. 27, 3547 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  77. D.J. Fernandez, L. M. Nieto, O. Rosas-Ortiz, Distorted Heisenberg algebra and coherent states for isospectral oscillator Hamiltonians. J. Phys. A Math. Gen. 28, 2693 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  78. J.O. Rosas-Ortiz, Fock-Bargmann representation of the distorted Heisenberg algebra. J. Phys. A Math. Gen. 29, 3281 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  79. M.S. Kumar, A. Khare, Coherent states for isospectral Hamiltonians. Phys. Lett. A 217, 73 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. D.J. Fernandez, V. Hussin, Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states. J. Phys. A Math. Gen. 32, 3603 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  81. D.J. Fernandez, V. Hussin, O. Rosas-Ortiz, Coherent states for Hamiltonians generated by supersymmetry. J. Phys. A Math. Teor. 40, 6491 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  82. D.J. Fernandez, O. Rosas-Ortiz, V. Hussin, Coherent states for SUSY partner Hamiltonians. J. Phys. Conf. Ser. 128, 012023 (2008)

    Article  Google Scholar 

  83. O. Rosas-Ortiz, O. Castaños, D. Schuch, New supersymmetry-generated complex potentials with real spectra. J. Phys. A Math. Theor. 48, 445302 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  84. A. Jaimes-Najera, O. Rosas-Ortiz, Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum. Ann. Phys. 376, 126 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  85. Z. Blanco-Garcia, O. Rosas-Ortiz, K. Zelaya, Interplay between Riccati, Ermakov and Schrödinger equations to produce complex-valued potentials with real energy spectrum. Math. Methods Appl. Sci. 1–14 (2018). https://doi.org/10.1002/mma.5069; arXiv:1804.05799

  86. O. Rosas-Ortiz, K. Zelaya, Bi-orthogonal approach to non-Hermitian Hamiltonians with the oscillator spectrum: generalized coherent states for nonlinear algebras. Ann. Phys. 388, 26 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  87. K. Zelaya, S. Dey, V. Hussin, O. Rosas-Ortiz, Nonclassical states for non-Hermitian Hamiltonians with the oscillator spectrum. arXiv:1707.05367

    Google Scholar 

  88. M. Orzag, S. Salamo, Squeezing and minimum uncertainty states in the supersymmetric harmonic oscillator. J. Phys. A Math. Gen. 21, L1059 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  89. G. Junker, P. Roy, Non-linear coherent states associated with conditionally exactly solvable problems. Phys. Lett. A 257, 113 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  90. B. Roy, P. Roy, New nonlinear coherent states and some of their nonclassical properties. J. Opt. B Quantum Semiclass. Opt. 2, 65 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  91. R. Roknizadeh, M.K. Tavassoly, The construction of some important classes of generalized coherent states: the nonlinear coherent states method. J. Phys. A Math. Gen. 37, 8111 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  92. R. Roknizadeh, M.K. Tavassoly, Representations of coherent and squeezed states in a f-deformed Fock space. J. Phys. A Math. Gen. 37, 5649 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  93. M.K. Tavassoly, New nonlinear coherent states associated with inverse bosonic and f-deformed ladder operators. J. Phys. A Math. Theor. 41, 285305 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  94. F. Bagarello, Extended SUSY quantum mechanics, intertwining operators and coherent states. Phys. Lett. A 372, 6226 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  95. S. Twareque 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 

  96. F. Bagarello, Vector coherent states and intertwining operators. J. Phys. A Math. Theor. 42, 075302 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  97. F. Bagarello, Quons, coherent states and intertwining operators. Phys. Lett. A 373, 2637 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  98. G.R. Honarasa, M.K. Tavassoly, M. Hatami, Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach. Opt. Commun. 282, 2192 (2009)

    Article  ADS  Google Scholar 

  99. O. Abbasi, M.K. Tavassoly, Superposition of two nonlinear coherent states \(\frac {\pi }{2}\) out of phase and their nonclassical properties. Opt. Commun. 282, 3737 (2009)

    Google Scholar 

  100. M.K. Tavassoly, On the non-classicality features of new classes of nonlinear coherent states. Opt. Commun. 283, 5081 (2010)

    Article  ADS  Google Scholar 

  101. O. Safaeian, M.K. Tavassoly, Deformed photon-added nonlinear coherent states and their non-classical properties. J. Phys. A Math. Theor. 44, 225301 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  102. M. Kornbluth, F. Zypman, Uncertainties of coherent states for a generalized supersymmetric annihilation operator. J. Math. Phys. 54, 012101 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  103. A. NoormandiPour, M.K. Tavassoly, f-deformed squeezed vacuum and first excited states, their superposition and corresponding nonclassical properties. Commun. Theor. Phys. 61, 521 (2014)

    Article  ADS  MATH  Google Scholar 

  104. V. Hussin, I. Marquette, Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential. SIGMA 7, 024 (2011)

    MATH  Google Scholar 

  105. M. Angelova, A. Hertz, V. Hussin, Squeezed coherent states and the one-dimensional Morse quantum system. J. Phys. A Math. Theor. 45, 244007 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  106. M. Angelova, A. Hertz, V. Hussin, Corrigendum: squeezed coherent states and the one-dimensional Morse quantum system. J. Phys. A Math. Theor. 46, 129501 (2013)

    Article  ADS  MATH  Google Scholar 

  107. K. Zelaya, O. Rosas-Ortiz, Z. Blanco-Garcia, S. Cruz y Cruz, Completeness and nonclassicality of coherent states for generalized oscillator algebras. Adv. Math. Phys. 2017, 7168592 (2017)

    Google Scholar 

  108. B. Mojarevi, A. Dehghani, R.J. Bahrbeig, Excitation on the para-Bose states: nonclassical properties. Eur. Phys. J. Plus 133, 34 (2018)

    Article  Google Scholar 

  109. P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1930)

    MATH  Google Scholar 

  110. P.A.M. Dirac, The Principles of Quantum Mechanics, 4th edn revised (Oxford University Press, Oxford, 1967)

    Google Scholar 

  111. R.H. Brown, The Intensity Interferometer. Its Application to Astronomy (Taylor and Francis Ltd, New York, 1974)

    Google Scholar 

  112. E.T. Jaynes, Quantum beats, in Foundations of Radiation Theory and Quantum Electrodynamics, ed. by A.O. Barut (Plenum Press, New York, 1980), pp. 37–43

    Chapter  Google Scholar 

  113. G.I. Taylor, Interference fringes with feeble light. Proc. Camb. Philos. Soc. Math. Phys. Sci. 15, 114 (1909)

    Google Scholar 

  114. J. Schwinger, The theory of quantized fields III. Phys. Rev. 91, 728 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  115. J.R. Klauder, Continuous-representation theory I. Postulates of continuous-representation theory. J. Math. Phys. 4, 1055 (1963)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  117. J.R. Klauder, E.C.G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968)

    Google Scholar 

  118. V. Fock, Verallgemeinerung und Loösung der Diracschen statistischen Gleichung. Z. Phys. 49, 39 (1928)

    MATH  Google Scholar 

  119. V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform. Commun. Pure Appl. Math. 14, 187 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  120. D.S. Saxon, Elementary Quantum Mechanics (Holden-Day, Inc., San Francisco, 1968)

    Google Scholar 

  121. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1964)

    MATH  Google Scholar 

  122. L.I. Schiff, Quantum Mechanics (McGraw-Hill Book Company, New York, 1949)

    Google Scholar 

  123. E. Schrödinger, Der stetige Übergang von der Mikro-zur Makromechanik. Naturwissenschaften 14, 664 (1926); English translation in E. Schrödinger, Collected Papers on Wave Mechanics. AMS/Chelsea Series, vol. 302, 3rd (Augmented) edn. (American Mathematical Society, Providence, 2003)

    Google Scholar 

  124. E. Schrödinger, Collected Papers on Wave Mechanics. AMS/Chelsea Series, vol. 302, 3rd (Augmented) edn. (American Mathematical Society, Providence, 2003)

    Google Scholar 

  125. L.I. Schiff, Quantum Mechanics, 3rd edn. (McGraw-Hill, Singapore, 1968)

    Google Scholar 

  126. M. Born, Zur quantenmechanik der stossvorgänge. Z. Phys. 37, 863 (1926); English translation in Quantum Theory and Measurement, ed. by J. Wheeler, W. Zurek (Princeton University Press, Princeton, 1983)

    Google Scholar 

  127. B. Mielnik, O. Rosas-Ortiz, Quantum mechanical laws, in Fundamental of Physics, vol 1. Encyclopedia of Life Support Systems (UNESCO, Paris, 2009), pp. 255–326

    Google Scholar 

  128. M. Born, Quantenmechanik der stossvorgänge. Z. Phys. 38, 803 (1926)

    Article  ADS  MATH  Google Scholar 

  129. W. Pauli, Über gasentartung und paramagnetismus. Z. Phys. 43, 81 (1927)

    Article  ADS  MATH  Google Scholar 

  130. E.H. Kennard, Zur Quantenmechanik einfacher Bewegungstypen. Z. Phys. 44, 326 (1927)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  132. K. Husimi, Miscellanea in elementary quantum mechanics II. Prog. Theor. Phys. 9, 381 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  133. I.R. Senitzky, Harmonic oscillator wave functions. Phys. Rev. 95, 1115 (1954)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  134. J. Plebański, Classical properties of oscillator wave packets. Bull. Acad. Polon. Sci. Cl. III 11, 213 (1954)

    MATH  Google Scholar 

  135. J. Plebański, On certain wave-packets. Acta Phys. Polon. XIV, 275 (1955)

    Google Scholar 

  136. L. Infeld, J. Plebański, On a certain class of unitary transformations. Acta Phys. Pol. XIV, 41 (1955)

    Google Scholar 

  137. J. Plebański, Wave functions of a harmonic oscillator. Phys. Rev. 101, 1825 (1956)

    Article  ADS  Google Scholar 

  138. S.T. Epstein, Harmonic oscillator wave packets. Am. J. Phys. 27, 291 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  139. S.M. Roy, V. Singh, Generalized coherent states and the uncertainty principle. Phys. Rev. D 25, 3413 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  140. M.M. Nieto, Displaced and squeezed number states. Phys. Lett. A 229, 135 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  141. M.M. Nieto, L.M. Simmons, Coherent states for general potentials I. Formalism. Phys. Rev. D 20, 1321 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  142. M.M. Nieto, L.M. Simmons, Coherent states for general potentials II. Confining one-dimensional examples. Phys. Rev. D 20, 1332 (1979)

    Google Scholar 

  143. M.M. Nieto, L.M. Simmons, Coherent states for general potentials III. Nonconfining one-dimensional examples. Phys. Rev. D 20, 1342 (1979)

    Google Scholar 

  144. M.M. Nieto, Coherent states for general potentials IV. Three-dimensional systems. Phys. Rev. D 22, 391 (1980)

    Google Scholar 

  145. V.P. Gutschick, M.M. Nieto, Coherent states for general potentials V. Time evolution. Phys. Rev. D 22, 403 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  146. M.M. Nieto, L.M. Simmons, V.P. Gutschick, Coherent states for general potentials VI. Conclusions about the classical motion and the WKB approximation. Phys. Rev. D 23, 927 (1981)

    Google Scholar 

  147. M. Combescure, A quantum particle in a quadrupole radio-frequency trap. Ann. Inst. Henri Poincare A 44, 293 (1986)

    MathSciNet  MATH  Google Scholar 

  148. M. Combescure, The quantum stability problem for some class of time-dependent Hamiltonians. Ann. Phys. 185, 86 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  149. V.N. Gheorghe, F. Vedel, Quantum dynamics of trapped ions. Phys. Rev. A 45, 4828 (1992)

    Article  ADS  Google Scholar 

  150. B.M. Mihalcea, A quantum parametric oscillator in a radiofrequency trap. Phys. Scr. 2009, 014006 (2009)

    Article  Google Scholar 

  151. F.G. Major, V.N. Gheorghe, G. Werth, Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement (Springer, Berlin, 2005)

    Google Scholar 

  152. R.d.J. León-Montiel, H.M. Moya-Cessa, Exact solution to laser rate equations: three-level laser as a Morse-like oscillator. J. Mod. Opt. 63, 1521 (2016)

    Google Scholar 

  153. L. Zhang, W. Zhang, Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator. Ann. Phys. 373, 424 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  154. A. Contreras-Astorga, J. Negro, S. Tristao, Confinement of an electron in a non-homogeneous magnetic field: integrable vs superintegrable quantum systems. Phys. Lett. A 380, 48 (2016)

    Article  ADS  MATH  Google Scholar 

  155. K. Zelaya, O. Rosas-Ortiz, Exactly solvable time-dependent oscillator-like potentials generated by Darboux transformations. J. Phys. Conf. Ser. 839, 012018 (2017)

    Article  Google Scholar 

  156. A. Contreras-Astorga, A time-dependent anharmonic oscillator. J. Phys. Conf. Ser. 839, 012019 (2017)

    Article  Google Scholar 

  157. H. Cruz, M. Bermúdez-Montaña, R. Lemus, Time-dependent local-to-normal mode transition in triatomic molecules. Mol. Phys. 116, 77 (2018)

    Article  ADS  Google Scholar 

  158. J.G. Hartley, J.R. Ray, Coherent states for the time-dependent harmonic oscillator. Phys. Rev. D 25, 382 (1982)

    Article  ADS  Google Scholar 

  159. A. Contreras-Astorga, D. Fernandez, Coherent states for the asymmetric penning trap. Int. J. Theor. Phys. 50, 2085 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  160. M. Combescure, D. Robert, Coherent States and Applications in Mathematical Physics (Springer, Netherlands, 2012)

    Book  MATH  Google Scholar 

  161. D. Afshar, S. Mehrabankar, F. Abbasnezhad, Entanglement evolution in the open quantum systems consisting of asymmetric oscillators. Eur. Phys. J. D 70, 64 (2016)

    Article  ADS  MATH  Google Scholar 

  162. B. Mihalcea, Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps. Ann. Phys. 388, 100 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  163. N. Ünal, Quasi-coherent states for the Hermite Oscillator. J. Math. Phys. 59, 062104 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  164. K. Zelaya, O. Rosas-Ortiz, Comment on “Quasi-coherent states for the Hermite oscillator” [J. Math. Phys. 59, 062104 (2018)]. J. Math. Phys. 60, 054101 (2019). arXiv:1810.03662

    Google Scholar 

  165. R. Razo, K. Zelaya, S. Cruz y Cruz, O. Rosas-Ortiz, in preparation

    Google Scholar 

  166. O. Castaños, D. Schuch, O. Rosas-Ortiz, Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations. J. Phys. A Math. Theor. 46, 075304 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  167. D. Schuch, O. Castaños, O. Rosas-Ortiz, Generalized creation and annihilation operators via complex nonlinear Riccati equations. J. Phys. Conf. Ser. 442, 012058 (2013)

    Article  MATH  Google Scholar 

  168. H. Cruz, D. Schuch, O Castaños, O. Rosas-Ortiz, Time-evolution of quantum systems via a complex nonlinear Riccati equation I. Conservative systems with time-independent Hamiltonian. Ann. Phys. 360, 44 (2015)

    Google Scholar 

  169. H. Cruz, D. Schuch, O Castaños, O. Rosas-Ortiz, Time-evolution of quantum systems via a complex nonlinear Riccati equation II. Dissipative systems. Ann. Phys. 373, 609 (2016)

    Google Scholar 

  170. S. Cruz y Cruz, Z. Gress, Group approach to the paraxial propagation of Hermite-Gaussian modes in a parabolic medium. Ann. Phys. 383, 257 (2017)

    Google Scholar 

  171. Z. Gress, S. Cruz y Cruz, A note on the off-axis Gaussian beams propagation in parabolic media. J. Phys. Conf. Ser. 839, 012024 (2017)

    Google Scholar 

  172. R. Razo, S. Cruz y Cruz, New confining optical media generated by Darboux transformations. J. Phys. Conf. Ser. 1194, 012091 (2019)

    Google Scholar 

  173. R. Román-Ancheyta, M. Berrondo, J. Récamier, Parametric oscillator in a Kerr medium: evolution of coherent states. J. Opt. Soc. Am. B 32, 1651 (2015)

    Article  ADS  Google Scholar 

  174. R. Román-Ancheyta, M. Berrondo, J. Récamier, Approximate yet confident solution for a parametric oscillator in a Kerr medium. J. Phys. Conf. Ser. 698, 012008 (2016)

    Article  Google Scholar 

  175. R. Román-Ancheyta, C. González-Gutiérrez, J. Récamier, Influence of the Kerr nonlinearity in a single nonstationary cavity mode. J. Opt. Soc. Am. B 34, 1170 (2017)

    Article  ADS  Google Scholar 

  176. R.d.J. León-Montiel, H.M. Moya-Cessa, Generation of squeezed Schrödinger cats in a tunable cavity filled with a Kerr medium. J. Opt. 17, 065202 (2015)

    Google Scholar 

  177. J. de Lucas, M. Tobolski, S. Vilariño, Geometry of Riccati equations over normed division algebras. J. Math. Anal. Appl. 440, 394 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  178. M.A. Rego-Monteiro, E.M.F. Curado, L.M.C.S. Rodrigues, Time evolution of linear and generalized Heisenberg algebra nonlinear Pöschl-Teller coherent states. Phys. Rev. A 96, 052122 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  179. D. Schuch, Quantum Theory from a Nonlinear Perspective. Riccati Equations in Fundamental Physics (Springer, Switzerland, 2018)

    Google Scholar 

  180. W. Heisenberg, Physics and Beyond, Encounters and Conversations (Harper and Row, Publishers, Inc., New York, 1971)

    Google Scholar 

  181. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927); English translation in NASA Technical Report Server, Document ID: 19840008978, web page https://ntrs.nasa.gov/search.jsp?R=19840008978, consulted December 2018

  182. P.A.M. Dirac, Quantum electrodynamics without dead wood. Phys. Rev. 139, B684 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  183. K. Przibram (ed.), Albert Einstein: Letters on Wave Mechanics. Correspondence with H.A. Lorentz, Max Planck, and Erwin Schrödinger (Philosophical Library, New York, 1967)

    Google Scholar 

  184. P. Carruthers, M.M. Nieto, Coherent states and the forced quantum oscillator. Am. J. Phys. 33, 537 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  185. L.S. Brown, Classical limit of the hydrogen atom. Am. J. Phys. 41, 525 (1973)

    Article  ADS  Google Scholar 

  186. J. Mostowski, On the classical limit of the Kepler problem. Lett. Math. Phys. 2, 1 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  187. D. Bhaumik, B. Dutta-Roy, G. Ghosh, Classical limit of the hydrogen atom. J. Phys. A Math. Gen. 19, 1355 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  188. J.-C. Gay, D. Delande, A. Bommier, Atomic quantum states with maximum localization on classical elliptical orbits. Phys. Rev. A 39, 6587 (1989)

    Article  ADS  Google Scholar 

  189. M. Nauenberg, Quantum wave packets on Kepler elliptic orbits. Phys. Rev. A 40, 1133 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  190. Z.D. Gaeta, C.R. Stroud, Jr., Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom. Phys. Rev. A 42, 6308 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  191. J.A. Yeazell, C.R. Stroud, Jr., Observation of fractional revivals in the evolution of a Rydberg atomic wave packet. Phys. Rev. A 43, 5153 (1991)

    Article  ADS  Google Scholar 

  192. I. Zaltev, W.M. Zhang, D.H. Feng, Possibility that Schrödinger’s conjecture for the hydrogen-atom coherent states is not attainable. Phys. Rev. A 50, R1973 (1994)

    Article  ADS  Google Scholar 

  193. S. Haroche, J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford University Press, Oxford, 2006)

    Book  MATH  Google Scholar 

  194. J.R. Klauder, Coherent states for the hydrogen atom. J. Phys. A Math. Gen. 29, L293 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  195. P. Majumdar, H.S. Sharatchandra, Coherent states for the hydrogen atom. Phys. Rev. A 56, R3322 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  196. B. Mielnik, J. Plebánski, Combinatorial approach to Baker-Campbell-Hausdorff exponents. Annales de l’I.H.P. Physique théorique 12, 215 (1970)

    Google Scholar 

  197. R. Gilmore, Baker-Campbell-Hausdorff formulas. J. Math. Phys. 15, 2090 (1974)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  198. M. Ban, Decomposition formulas for su(1,  1) and su(2) Lie algebras and their applications in quantum optics. J. Opt. Soc. Am. B 10, 1347 (1993)

    Google Scholar 

  199. A. DasGupta, Disentanglement formulas: an alternative derivation and some applications to squeezed coherent states. Am. J. Phys. 64, 1422 (1996)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  201. A.M. Perelomov, Generalized coherent states and some of their applications (in Russian). Moscow Usp. Fiz. Nauk. 123, 23 (1977); English translation in Sov. Phys. Usp. 20, 703 (1977)

    Google Scholar 

  202. A.M. Perelomov, Generalized Coherent States and Their Applications (Springer, Heidelberg, 1986)

    Book  MATH  Google Scholar 

  203. R. Gilmore, On the properties of coherent states. Rev. Mex. Fis. 23, 143 (1974)

    Google Scholar 

  204. W.M. Zhang, D.H. Feng, R. Gilmore, Coherent states-theory and some applications. Rev. Mod. Phys. 62, 867 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  205. C.M. Caves, B.L. Schumaker, New formalism for two-photon quantum optics I. Quadrature phases and squeezed states. Phys. Rev. A 31, 3068 (1985)

    Google Scholar 

  206. B.L. Schumaker, C.M. Caves, New formalism for two-photon quantum optics II. Mathematical foundation and compact notation. Phys. Rev. A 31, 3093 (1985)

    Google Scholar 

  207. A.O. Barut, L. Girardello, New ‘coherent’ states associated with noncompact groups. Commun. Math. Phys. 21, 41 (1971)

    Article  ADS  MATH  Google Scholar 

  208. J.R. Klauder, B.-S. Skagerstam, Coherent States: Applications in Physics and Mathematical Physics (World Scientific, Singapore, 1985)

    Book  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  210. L. Fonda, N. Mankoc-Brostnik, M. Rosina, Coherent rotational states: their formation and detection. Phys. Rep. 158, 159 (1988)

    Article  ADS  Google Scholar 

  211. S.T. Ali, J.-P. Antoine, J.-P. Gazeau, U.A. Mueller, Coherent states and their generalizations: a mathematical overview. Rev. Math. Phys. 7, 1013 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  212. S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets, and Their Generalizations, 2nd edn. (Springer, New York, 1999)

    MATH  Google Scholar 

  213. J. Bertrand, P. Bertrand, J. Ovarlez, The Mellin transform, in The Transforms and Applications Handbook, ed. by A.D. Poularikas (CRC Press, Boca Raton, 2000)

    MATH  Google Scholar 

  214. H. Rosu, C. Castro, q-deformation by intertwining with application to the singular oscillator. Phys. Lett. A 264, 350 (2000)

    Google Scholar 

  215. E.T. Jaynes, F.W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89 (1963)

    Article  Google Scholar 

  216. B. Buck, C.V. Sukumar, Exactly soluble model of atom-phonon coupling showing periodic decay and revival. Phys. Lett. A 81, 132 (1981)

    Article  ADS  Google Scholar 

  217. C.V. Sukumar, B. Buck, Multi-phonon generalisation of the Jaynes-Cummings model. Phys. Lett. A 83, 211 (1981)

    Article  ADS  Google Scholar 

  218. G. Bastard, Superlattice band structure in the envelope-function approximation. Phys. Rev. B 24, 5693 (1981)

    Article  ADS  Google Scholar 

  219. G. Bastard, Theoretical investigations of superlattice band structure in the envelope-function approximation. Phys. Rev. B 24, 5693 (1982)

    Article  ADS  Google Scholar 

  220. V. Milanović, Z. Ikonić, Generation of isospectral combinations of the potential and the effective-mass variations by supersymmetric quantum mechanics. J. Phys. A Math. Gen. 32, 7001 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  221. A. de Souza Dutra, C.A.S. Almeida, Exact solvability of potentials with spatially dependent effective masses. Phys. Lett. A 275, 25 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  222. B. Roy, Lie algebraic approach to singular oscillator with a position-dependent mass. Eur. Phys. Lett. 72, 1 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  223. A. Ganguly, M.V. Ioffe, L.M. Nieto, A new effective mass Hamiltonian and associated Lamé equation: bound states. J. Phys. A Math. Gen. 39, 14659 (2006)

    Article  ADS  MATH  Google Scholar 

  224. O. Mustafa, S.H. Mazharimousavi, Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe. Phys. Lett. A 358, 259 (2006)

    Article  ADS  MATH  Google Scholar 

  225. S. Cruz y Cruz, J. Negro, L.M. Nieto, Classical and quantum position-dependent mass harmonic oscillators. Phys. Lett. A 369, 400 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  226. S. Cruz y Cruz, S. Kuru, J. Negro, Classical motion and coherent states for Pöschl-Teller potentials. Phys. Lett. A 372, 1391 (2008)

    Google Scholar 

  227. S. Cruz y Cruz, J. Negro, L.M. Nieto, On position-dependent mass harmonic oscillators. J. Phys. Conf. Ser. 128, 012053 (2008)

    Google Scholar 

  228. O. Mustafa, S.H. Mazharimousavi, A singular position-dependent mass particle in an infinite potential well. Phys. Lett. A 373, 325 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  229. S. Cruz y Cruz, O. Rosas-Ortiz, Dynamical equations, invariants and spectrum generating algebras of mechanical systems with position-dependent mass. SIGMA 9, 004 (2013)

    Google Scholar 

  230. B. Bagchi, S. Das, S. Ghosh, S. Poria, Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator. J. Phys. A Math. Theor. 46, 032001 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  231. M. Lakshmanan, K. Chandrasekar, Generating finite dimensional integrable nonlinear dynamical systems. Eur. Phys. J. Spec. Top. 222, 665 (2013)

    Article  Google Scholar 

  232. S. Cruz y Cruz, Factorization method and the position-dependent mass problem, in Geometric Methods in Physics, ed. by P. Kielanowski, S. Ali, A. Odzijewicz, M. Schlichenmaier, T. Voronov. Trends in Mathematics (Birkhäuser, Basel, 2013), pp. 229–237

    Google Scholar 

  233. B.G. da Costa, E. Borges, Generalized space and linear momentum operators in quantum mechanics. J. Math. Phys. 55, 062105 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  234. S. Cruz y Cruz, C. Santiago-Cruz, Bounded motion for classical systems with position-dependent mass. J. Phys. Conf. Ser. 538, 012006 (2014)

    Google Scholar 

  235. A.G. Nikitin, T.M. Zasadko, Superintegrable systems with position dependent mass. J. Math. Phys. 56, 042101 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  236. O. Mustafa, Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability. J. Phys. A Math. Theor. 48, 225206 (2015)

    Article  ADS  MATH  Google Scholar 

  237. D. Ghosch, B. Roy, Nonlinear dynamics of classical counterpart of the generalized quantum nonlinear oscillator driven by position dependent mass. Ann. Phys. 353, 222 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  238. B. Bagchi, A.G. Choudhury, P. Guha, On quantized Liénard oscillator and momentum dependent mass. J. Math. Phys. 56, 012105 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  239. N. Amir, S. Iqbal, Algebraic solutions of shape-invariant position-dependent effective mass systems. J. Math. Phys. 57, 062105 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  240. C. Santiago-Cruz, Isospectral trigonometric Pöschl-Teller potentials with position dependent mass generated by supersymmetry. J. Phys. Conf. Ser. 698, 012028 (2016)

    Article  Google Scholar 

  241. R. Bravo, M.S. Plyushchay, Position-dependent mass, finite-gap systems, and supersymmetry. Phys. Rev. D 93, 105023 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  242. A.G. Nikitin, Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses. J. Math. Phys. 58, 083508 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  243. B.G. da Costa, E.P. Borges, A position-dependent mass harmonic oscillator and deformed space. J. Math. Phys. 59, 042101 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  244. A.G.M. Schmidt, A.L. de Jesus, Mapping between charge-monopole and position-dependent mass system. J. Math. Phys. 59, 102101 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  245. O.Cherroud, A.-A. Yahiaoui, M. Bentaiba, Generalized Laguerre polynomials with position-dependent effective mass visualized via Wigner’s distribution functions. J. Math. Phys. 58, 063503 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  246. S. Cruz y Cruz, C. Santiago-Cruz, Position dependent mass Scarf Hamiltonians generated via the Riccati equation. Math. Methods Appl. Sci. 1–16 (2018). https://doi.org/10.1002/mma.5068

  247. K.B. Wolf, Geometric Optics on Phase Space. Texts and Monographs in Physics (Springer, Berlin, 2004)

    Google Scholar 

  248. A. de Souza Dutra, J.A. de Oliviera, Wigner distribution for a class of isospectral position-dependent mass systems. Phys. Scr. 78, 035009 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  249. S. Cruz y Cruz, O. Rosas-Ortiz, Position dependent mass oscillators and coherent states. J. Phys. A Math. Theor. 42, 185205 (2009)

    Google Scholar 

  250. C. Chithiika Ruby, M. Senthilvelan, On the construction of coherent states of position dependent mass Schrödinger equation endowed with effective potential. J. Math. Phys. 51, 052106 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  251. S.-A. Yahiaoui, M. Bentaiba, Pseudo-Hermitian coherent states under the generalized quantum condition with position-dependent mass. J. Phys. A Math. Gen. 45, 444034 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  252. S.-A. Yahiaoui, M. Bentaiba, New SU(1,  1) position-dependent effective mass coherent states for a generalized shifted harmonic oscillator. J. Phys. A Math. Gen. 47, 025301 (2014)

    Google Scholar 

  253. N. Amir, S. Iqbal, Barut-Girardello coherent states for nonlinear oscillator with position-dependent mass. Commun. Theor. Phys. 66, 41 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  254. S.-A. Yahiaoui, M. Bentaiba, Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states. J. Math. Phys. 58, 063507 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  255. N. Amir, S. Iqbal, Coherent states of nonlinear oscillators with position-dependent mass: temporal stability and fractional revivals. Commun. Theor. Phys. 68, 181 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  256. S. Cruz y Cruz, O. Rosas-Ortiz, SU(1,  1) coherent states for position-dependent mass singular oscillators. Int. J. Theor. Phys. 50, 2201 (2011)

    Google Scholar 

  257. D. Dragoman, M. Dragoman, Quantum–Classical Analogies (Springer, New York, 2004)

    Book  MATH  Google Scholar 

  258. H. Rauch, S.A. Werner, Neutron Interferometry: Lessons in Experimental Quantum Mechanics, Wave-Particle Duality, and Entanglement, 2nd edn. (Oxford University Press, Oxford, 2015)

    Book  MATH  Google Scholar 

  259. F.D. Belgiorno, S.L. Cacciatori, D. Faccio, Hawking Radiation. From Astrophysical Black Holes to Analogous Systems in Lab (World Scientific, Singapore, 2019)

    Google Scholar 

  260. L.M. Procopio, O. Rosas-Ortiz, V. Velázquez, On the geometry of spatial biphoton correlation in spontaneous parametric down conversion. Math. Methods Appl. Sci. 38, 2053 (2015)

    Article  ADS  MATH  Google Scholar 

  261. O. Calderón-Losada, J. Flóres, J.P. Villabona-Monsalve, A. Valencia, Measuring different types of transverse momentum correlations in the biphoton’s Fourier plane. Opt. Lett. 41, 1165 (2016)

    Article  ADS  Google Scholar 

  262. J. López-Durán, O. Rosas-Ortiz, Quantum and Classical Correlations in the Production of Photon-Pairs with Nonlinear Crystals. J. Phys. Conf. Ser. 839, 012022 (2017)

    Article  Google Scholar 

  263. C. Couteau, Spontaneous parametric down-conversion. Contemp. Phys. 59, 291 (2018)

    Article  ADS  Google Scholar 

  264. K. Okamoto, Fundamentals of Optical Waveguides, 2nd edn. (Elsevier, California, 2011)

    Google Scholar 

  265. S. Cruz y Cruz, R. Razo, Wave propagation in the presence of a dielectric slab: the paraxial approximation. J. Phys. Conf. Ser. 624, 012018 (2015)

    Google Scholar 

  266. S. Cruz y Cruz, O. Rosas-Ortiz, Leaky modes of waveguides as a classical optics analogy of quantum resonances. Adv. Math. Phys. 2015, 281472 (2015)

    Google Scholar 

  267. G.R. Honarasa, M. Hatami, M.K. Tavassoly, Quantum squeezing of dark solitons in optical fibers. Commun. Theor. Phys. 56, 322 (2011)

    Article  MATH  Google Scholar 

  268. O. Rosas-Ortiz, S. Cruz y Cruz, Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials, arXiv:1805.00058

    Google Scholar 

  269. W. Walasik, B. Midya, L. Feng, N.M. Litchinitser, Supersymmetry-guided method for mode selection and optimization in coupled systems. Opt. Lett. 43, 3758 (2018)

    Article  ADS  Google Scholar 

  270. A. Contreras-Astorga, V. Jakubský, Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry. Phys. Rev. A 99, 053812 (2019). arXiv:1808.08225

    Google Scholar 

  271. R. Gilmore, C.M. Bowden, L.M. Narducci, Classical-quantum correspondence for multilevel systems. Phys. Rev. A 12, 1019 (1975)

    Article  ADS  Google Scholar 

  272. S. Cruz y Cruz, B. Mielnik, Non-inertial quantization: truth or illusion? J. Phys. Conf. Ser. 698, 012002 (2016)

    Google Scholar 

  273. G. Cozzella, A.G.S. Landulfo, G.E.A. Matsas, D.A.T. Vanzella, Proposal for observing the Unruh effect using classical electrodynamics. Phys. Rev. Lett. 118, 161102 (2017)

    Article  ADS  Google Scholar 

  274. A.M. Cetto, L. de la Peña, Real vacuum fluctuations and virtual Unruh radiation. Fortschr. Phys. 65, 1600039 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  275. J.A. Rosabal, New perspective on the Unruh effect. Phys. Rev. D 98, 056015 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  276. D. Bermudez, U. Leonhardt, Hawking spectrum for a fiber-optical analog of the event horizon. Phys. Rev. A 93, 053820 (2016)

    Article  ADS  Google Scholar 

  277. D. Bermudez, U. Leonhardt, Resonant Hawking radiation as an instability, arXiv:1808.02210

    Google Scholar 

  278. J. Drori, Y. Rosenberg, D. Bermudez, Y. Silbergerg, U. Leonhardt, Observation of stimulated hawking radiation in optics, arXiv:1808.09244

    Google Scholar 

  279. M.F. Bocko, R. Onofrio, On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress. Rev. Mod. Phys. 68, 755 (1996)

    Article  ADS  Google Scholar 

  280. A.A. Clerk, M.H. Devoret, S.M. Girvin, F. Marquardt, R.J. Schoelkopf, Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  281. C. Guerlin, J. Bernu, S. Deléglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, S. Haroche, Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889 (2007)

    Article  ADS  Google Scholar 

  282. C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J.-M. Raimond, S. Haroche, Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73 (2011)

    Article  ADS  Google Scholar 

  283. D. Oriti, R. Pereira, L. Sindoni, Coherent states in quantum gravity: a construction based on the flux representation of loop quantum gravity. J. Phys. A Math. Theor. 45, 244004 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  284. T. Thiemann, Gauge field theory coherent states (GCS): I. General properties. Class. Quantum Grav. 18, 2025 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  285. T. Thiemann, O. Winkler, Gauge field theory coherent states (GCS): II. Peakedness properties. Class. Quantum Grav. 18, 2561 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  286. T. Thiemann, O. Winkler, Gauge field theory coherent states (GCS): III. Ehrenfest theorems. Class. Quantum Grav. 18, 4629 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  287. T. Thiemann, O. Winkler, Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit. Class. Quantum Grav. 18, 4997 (2001)

    Article  MATH  Google Scholar 

  288. B.C. Hall, Coherent states and the quantization of (1+1)-dimensional Yang-Mills theory. Rev. Math. Phys. 13, 1281 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  289. J.G. Leopold, I.C. Percival, Microwave ionization and excitation of Rydberg atoms. Phys. Rev. Lett. 41, 944 (1978)

    Article  ADS  Google Scholar 

  290. E. Lee, A.F. Brunello, D. Farrelly, Coherent states in a Rydberg atom: classical mechanics. Phys. Rev. A 55, 2203 (1997)

    Article  ADS  Google Scholar 

  291. D. Meschede, H. Walther, G. Müller, One-atom maser. Phys. Rev. Lett. 54, 551 (1985)

    Article  ADS  Google Scholar 

  292. M. Brune, J.M. Raimond, P. Goy, L. Davidovich, S. Haroche, Realization of a two-photon maser oscillator. Phys. Rev. Lett. 59, 1899 (1987)

    Article  ADS  Google Scholar 

  293. E.J. Galvez, B.E. Sauer, L. Moorman, P.M. Koch, D. Richards, Microwave ionization of H atoms: breakdown of classical dynamics for high frequencies. Phys. Rev. Lett. 61, 2011 (1988)

    Article  ADS  Google Scholar 

  294. D.J. Wineland, C. Monroe, W.M. Itano, D. Leibfried, B.E. King, D.M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998)

    Article  MATH  Google Scholar 

  295. L. Davidovich, Quantum optics in cavities and the classical limit of quantum mechanics. AIP Conf. Proc. 464, 3 (1999)

    Article  ADS  Google Scholar 

  296. J.M. Raimond, M. Brune, S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  297. H. Moya-Cessa, Decoherence in atom-field interactions: a treatment using superoperator techniques. Phys. Rep. 432, 1 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  298. Y. Berubelauzire, V. Hussin, L.M. Nieto, Annihilation operators and coherent states for the Jaynes-Cummings model. Phys. Rev. A 50, 1725 (1994)

    Article  ADS  Google Scholar 

  299. M. Daoud, V. Hussin, General sets of coherent states and the Jaynes-Cummings model. J. Phys. A Math. Gen. 35, 7381 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  300. V. Hussin, L.M. Nieto, Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation. J. Math. Phys. 46, 122102 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  301. J.M. Fink, M. Göpl, M. Baur, R. Bianchetti, P.J. Leek, A. Blais, A. Wallraff, Climbing the Jaynes-Cummings ladder and observing its \(\sqrt {n}\) nonlinearity in a cavity QED system. Nature 454, 315 (2008)

    Google Scholar 

  302. F.T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, Atomic coherent state in quantum optics. Phys. Rev. A 6, 2211 (1974)

    Article  ADS  Google Scholar 

  303. J.-P. Gazeau, V. Hussin, Poincaré contraction of SU(1, l) Fock-Bargmann structure. J. Phys. A Math. Gen 25, 1549 (1992)

    Article  ADS  MATH  Google Scholar 

  304. N. Alvarez, V. Hussin, Generalized coherent and squeezed states based on the h(1) ⊕ su(2) algebra. J. Math. Phys. 43, 2063 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  305. A. Wünsche, Duality of two types of SU(1,  1) coherent states and an intermediate type. J. Opt. B Quantum Semiclass. Opt. 5, S429 (2003)

    Article  Google Scholar 

  306. S.R. Miry, M.K. Tavassoly, Generation of a class of SU(1,  1) coherent states of the Gilmore-Perelomov type and a class of SU(2) coherent states and their superposition. Phys. Scr. 85, 035404 (2012)

    Google Scholar 

  307. A. Karimi, M.K. Tavassoly, Quantum engineering and nonclassical properties of SU(1,  1) and SU(2) entangled nonlinear coherent states. J. Opt. Soc. Am. B 31, 2345 (2014)

    Google Scholar 

  308. D.N. Daneshmand, M.K. Tavassoly, Generation of SU(1,  1) and SU(2) entangled states in a quantized cavity field by strong-driving-assisted classical field approach. Laser Phys. 25, 055203 (2015)

    Google Scholar 

  309. O. Rosas-Ortiz, S. Cruz y Cruz, M. Enríquez, SU(1,  1) and SU(2) approaches to the radial oscillator: generalized coherent states and squeezing of variances. Ann. Phys. 346, 373 (2016)

    Google Scholar 

  310. B.C. Sanders, Review of entangled coherent states. J. Phys. A Math. Theor. 45, 244002 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  311. L. Li, Y.O. Dudin, A. Kuzmich, Entanglement between light and an optical atomic excitation. Nature 498, 466 (2013)

    Article  ADS  Google Scholar 

  312. S. Dey, V. Hussin, Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations. Phys. Rev. D 91, 124017 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  313. A. Motamedinasab, D. Afshar, M. Jafarpour, Entanglement and non-classical properties of generalized supercoherent states. Optik 157, 1166 (2018)

    Article  ADS  Google Scholar 

  314. V. Spiridonov, Universal superpositions of coherent states and self-similar potentials. Phys. Rev. A 52, 1909 (1995)

    Article  ADS  Google Scholar 

  315. S. Dey, A. Fring, V. Hussin, A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length, arXiv:1801.01139

    Google Scholar 

  316. S.T. Ali, R. Roknizadeh, M.K. Tavassoly, Representations of coherent states in non-orthogonal bases. J. Phys. A Math. Gen. 37, 4407 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  317. S. Dey, V. Hussin, Noncommutative q-photon-added coherent states. Phys. Rev. A 93, 053824 (2016)

    Article  ADS  Google Scholar 

  318. S. Dey, A. Fring, V. Hussin, Nonclassicality versus entanglement in a noncommutative space. Int. J. Mod. Phys. B 31, 1650248 (2017)

    Article  ADS  MATH  Google Scholar 

  319. A. Hertz, S. Dey, V. Hussin, H. Eleuch, Higher order nonclassicality from nonlinear coherent states for models with quadratic spectrum. Symmetry-Basel 8, 36 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  320. K. Zelaya, S. Dey, V. Hussin, Generalized squeezed states. Phys. Lett. A 382, 3369 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  321. C. Aragone, F. Zypman, Supercoherent states. J. Phys. A Math. Gen. 19, 2267 (1986)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  322. A.M. El Gradechi, L.M. Nieto, Supercoherent states, super-Kähler geometry and geometric quantization. Commun. Math. Phys. 175, 521 (1996)

    Article  ADS  MATH  Google Scholar 

  323. J. Jayaraman, R. de Lima Rodrigues, A SUSY formulation ála Witten for the SUSY isotonic oscillator canonical supercoherent states. J. Phys. A Math. Gen. 32, 6643 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  324. N. Alvarez-Moraga, V. Hussin, sh(2∕2) superalgebra eigenstates and generalized supercoherent and supersqueezed states. Int. J. Theor. Phys. 43, 179 (2004)

    Google Scholar 

  325. L.M. Nieto, Coherent and supercoherent states with some recent applications. AIP Conf. Proc. 809, 3 (2006)

    Article  ADS  MATH  Google Scholar 

  326. A.H. El Kinani, M. Daoud, Generalized intelligent states for nonlinear oscillators. Int. J. Mod. Phys. B 15, 2465 (2001)

    Article  ADS  Google Scholar 

  327. B. Midya, B. Roy, A. Biswas, Coherent state of a nonlinear oscillator and its revival dynamics. Phys. Scr. 79, 065003 (2009)

    Article  ADS  MATH  Google Scholar 

  328. V.C. Ruby, S. Karthiga, M. Senthilevelan, Ladder operators and squeezed coherent states of a three-dimensional generalized isotonic nonlinear oscillator. J. Phys. A Math. Theor. 46, 025305 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  329. B. Roy, P. Roy, Gazeau-Klauder coherent state for the Morse potential and some of its properties. Phys. Lett. A 296, 187 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  330. A. Wünsche, Higher-order uncertainty relations. J. Mod. Opt. 53, 931 (2006)

    Article  ADS  MATH  Google Scholar 

  331. M.K. Tavassoly, Gazeau-Klauder squeezed states associated with solvable quantum systems. J. Phys. A Math. Gen. 39, 11583 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  332. L. Dello Sbarba, V. Hussin, Degenerate discrete energy spectra and associated coherent states. J. Math. Phys. 48, 012110 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  333. M. Angelova, V. Hussin, Generalized and Gaussian coherent states for the Morse potential. J. Phys. A Mat. Theor. 41, 304016 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  334. G.R. Honarasa, M.K. Tavassoly, M. Hatami, R. Roknizadeh, Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties. Phys. A 390, 1381 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  335. M.K. Tavassoly, H.R. Jalai, Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties: factorization method. Chin. Phys. B 22, 084202 (2013)

    Article  Google Scholar 

  336. M.N. Hounkonnoua, S. Arjikab, E. Baloïtcha, Ps̈chl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics, and geometry. J. Math. Phys. 55, 123502 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  337. S.E. Hoffmann, V. Hussin, I. Marquette, Y.-Z. Zhang, Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials. J. Phys. A Math. Theor. 51, 085202 (2018)

    Article  MATH  Google Scholar 

  338. S.E. Hoffmann, V. Hussin, I. Marquette, Y.-Z. Zhang, Coherent states for ladder operators of general order related to exceptional orthogonal polynomials. J. Phys. A Math. Theor. 51, 315203 (2018). arXiv:1803.01318

    Google Scholar 

  339. J.-P. Antoine, J.-P. Gazeau, P. Monceau, J.R. Klauder, K.A. Penson, Temporally stable coherent states for infinite well and Pöschl–Teller potentials. J. Math. Phys. 42, 2349 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  340. H. Bergeron, J.-P. Gazeau, P. Siegl, A. Youssef, Semi-classical behavior of Pöschl-Teller coherent states. Europhys. Lett. 92, 60003 (2011)

    Article  ADS  Google Scholar 

  341. J.-P. Gazeau, M. del Olmo, Pissot q-coherent states quantization of the harmonic oscillator. Ann. Phys. 330, 220 (2012)

    Article  ADS  MATH  Google Scholar 

  342. J.-P. Gazeau, Coherent States in Quantum Physics (Wiley, Weinheim, 2009)

    Book  Google Scholar 

Download references

Acknowledgements

Financial support from Ministerio de Economía y Competitividad (Spain) grant number MTM2014-57129-C2-1-P, Consejería de Educación, Junta de Castilla y León (Spain) grant number VA057U16, and Consejo Nacional de Ciencia y Tecnología (México) project A1-S-24569 is acknowledged.

Author information

Authors and Affiliations

  1. Physics Department, Cinvestav, México City, Mexico

    Oscar Rosas-Ortiz

Authors
  1. Oscar Rosas-Ortiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oscar Rosas-Ortiz .

Editor information

Editors and Affiliations

  1. Department of Physics, Ankara University, Ankara, Turkey

    Şengül Kuru

  2. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Javier Negro

  3. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Luis M. Nieto

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rosas-Ortiz, O. (2019). Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations. In: Kuru, Ş., Negro, J., Nieto, L. (eds) Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20087-9_7

Download citation

Publish with us

Policies and ethics

Search

Navigation