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Regarding Nonstationary Quadratic Quantum Systems

  • Sh. M. NagiyevEmail author
  • A. I. Ahmadov
  • V. A. Tarverdiyeva
  • Sh. A. Amirova
QUANTUM ELECTRONICS
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With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.

Keywords

nonstationary quadratic systems evolution operator invariants wave functions unitary connection 

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References

  1. 1.
    V. G. Bagrov, D. M. Gitman, and A. S. Pereira, Usp. Fiz. Nauk, 184, No. 9, 961–966 (2014).CrossRefGoogle Scholar
  2. 2.
    Sh. M. Nagiyev, Teor. Mat. Fiz., 194, No. 2, 364–380 (2018).CrossRefGoogle Scholar
  3. 3.
    M. V. Berry and N. L. Balazs, Am. J. Phys., 47, No. 3, 264–267 (1979).ADSCrossRefGoogle Scholar
  4. 4.
    V. V. Dodonov, V. I. Manko, and O. V. Shakhmistova, Phys. Lett. A, 102, No. 7, 295–297 (1984).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    I. Guedes, Phys. Rev. A, 63, No. 3, 034102 (2001).ADSCrossRefGoogle Scholar
  6. 6.
    M. Feng, Phys. Rev. A, 64, No. 3, 034101 (2002).ADSCrossRefGoogle Scholar
  7. 7.
    P.-G. Luan and C.-S. Tang, Phys. Rev. A, 71, No. 1, 014101 (2005); arXiv:quant-ph/0309174.Google Scholar
  8. 8.
    K. Husimi, Progr. Theor. Phys., 9, 381–402 (1953).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).zbMATHGoogle Scholar
  10. 10.
    V. S. Popov and A. M. Perelomov, Zh. Eksp. Teor. Fiz., 56, No. 4, 1375–1390 (1969).Google Scholar
  11. 11.
    А. R. Lewis and W. B. Riesenfeld, J. Math. Phys., 12, 2040–2043 (1971).CrossRefGoogle Scholar
  12. 12.
    V. V. Dodonov and V. I. Man’ko, in: Proc. P. N. Lebedev Physical Institute of the Academy of Sciences, Vol. 183 (1987), p.182.Google Scholar
  13. 13.
    I. A. Pedrosa, Phys. Rev. A, 55, No. 4, 3219–3221 (1997).ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    R. Cordero-Soto, E. Suazo, and S. K. Suslov, Ann. Phys., 325, 1884–1912 (2010).ADSCrossRefGoogle Scholar
  15. 15.
    K. H. Yeon, H. Ju. Kim, C. I. Um, et al., Phys. Rev. A, 50, No. 2, 1035–1039 (1994).ADSCrossRefGoogle Scholar
  16. 16.
    D.-Y. Song, J. Phys. A, 32, 3449–3456 (1999).ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    P. Camiz, A. Gerardi, C. Marchioro, et al., J. Math., 12, 2040–2043 (1971).ADSGoogle Scholar
  18. 18.
    Sh. M. Nagiyev and K. Sh. Jafarova, Phys. Lett. A, 377, No. 10–11, 747–752 (2013).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Sh. M. Nagiyev, Teor. Mat. Fiz., 188, No. 1, 76–84 (2016).CrossRefGoogle Scholar
  20. 20.
    V. G. Bagrov, D. M. Gitman, I. M. Ternov, et al., Exact Solutions of Relativistic Wave Equations [in Russian], Nauka, Novosibirsk (1982).Google Scholar
  21. 21.
    V. G. Bagrov, Russ. Phys. J., 61, No. 3, 403–411 (2018).CrossRefGoogle Scholar
  22. 22.
    V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Teor. Mat. Fiz., 87, No. 3, 426–433 (1991).CrossRefGoogle Scholar
  23. 23.
    V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., 32, No. 11, 112–114 (1989).Google Scholar
  24. 24.
    I. A. Malkin and V. I. Man’ko. Dynamical Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).Google Scholar
  25. 25.
    G. Schrade, V. I. Manko, W. P. Schleich, and R. J. Glauber, Quantum Semiclass. Opt., 7, 307–325 (1995).ADSCrossRefGoogle Scholar
  26. 26.
    O. Castanos, S. Hacyan, R. Lopez-Pena, and V. I. Manko, J. Phys. A, 31, 1227 (1998).ADSCrossRefGoogle Scholar
  27. 27.
    A. M. Perelomov and V. S. Popov, Teor. Mat. Fiz., 3, No. 3, 377–391 (1970).CrossRefGoogle Scholar
  28. 28.
    F. J. Dyson, Phys. Rev., 75, No. 1, 1736–1755 (1949).ADSCrossRefGoogle Scholar
  29. 29.
    A. R. P. Rau and K. Unnikrishan, Phys. Lett. A, 222, 304–308 (1996).ADSMathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sh. M. Nagiyev
    • 1
    Email author
  • A. I. Ahmadov
    • 2
  • V. A. Tarverdiyeva
    • 1
  • Sh. A. Amirova
    • 1
  1. 1.Institute of Physics of the National Academy of Sciences of AzerbaijanBakuAzerbaijan
  2. 2.Baku State UniversityBakuAzerbaijan

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