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Path Integral of Time-Dependent Modified Caldirola–Kanai Oscillator

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Abstract

We evaluate the propagator, wave function and the uncertainty relation for a time-dependent damped Harmonic oscillator. We also analyze the classical solution of the quantum systems.

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References

  1. Marshall J.T., Pell J.L.: Path integrals evaluation of the space-tome propagator for quadratic hamiltonian systems. J. Math. Phys. 20, 1297 (1979)

    Article  MathSciNet  Google Scholar 

  2. Grosche, C.: An Introduction into the Feynman Path Integral. ICTP Lecture Note (1979)

  3. Grothaus, M.: The Feynman integral for time-dependent anharmonic oscillator. ICTP, Lecture Note, Trieste, p. 24 (1996)

  4. Duru I.H., Kleinert H.: Solution of the path integrals for the H-Atom. Phys. Lett. B 84, 185 (1979)

    Article  MathSciNet  Google Scholar 

  5. Das A.: Field Theory, A Path Integral Approach, p. 62. World Scientific Publishing Company Limited, Singapore (1993)

    Book  Google Scholar 

  6. Nash C.: Relativistic Quantum Fields, p. 24. Academic Press, London (1978)

    Google Scholar 

  7. Ituen, E.E.: Ph.D thesis, Department of Physics, University of Ibadan, Nigeria (1977)

  8. Hanc J., Taylor E.F., Tuleja S.: Deriving Lagrange equation using Elementary Calculus. Am. J. Phys. 72(4), 510 (2004)

    Article  Google Scholar 

  9. Hanc J., Taylor E.F., Tuleja S.: Variational Mechanics in one and two dimensions. Am. J. Phys. 73, 607 (2005)

    Article  Google Scholar 

  10. Khandekar D.C., Lawande S.V.: Exact solution of a time-dependent quantal harmonic oscillator with damping and a perturbative force. J. Math. Phys. 20, 1870 (1979)

    Article  MathSciNet  Google Scholar 

  11. Kim S.P., Satana A.E., Khanna F.C.: Decoherence of quantum damped oscillators. J. Korean Phys. Soc. 43, 452 (2003)

    Google Scholar 

  12. Caldirola, P.: Nuovo Cimento, Firze Conservative nella meccanica quantistica. 18, 393 (1941)

  13. Kanai E.: On the quantization of the dissipative systems. Prog. Theor. Phys. 3, 440 (1948)

    Article  Google Scholar 

  14. Lewis H.R.: Exact invariants for the time-dependent harmonic oscillator. Phys. Rev. Lett. 27, 510 (1967)

    Article  Google Scholar 

  15. Lewis H.R. Jr, Riesenfield W.B.: An exact quantum theory of a time-dependent oscillator and a charge particle in a time dependent electromagnetic field. J. Math. Phys. 10, 1458 (1969)

    Article  Google Scholar 

  16. Um C.I., Yeon K.H., George T.F.: The quantum harmonic oscillator. Phys. Rep. 362, 63 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Um C.I., Yeon K.H.: Quantum theory of the harmonic oscillator in non-conservative systems. Korean Phys. Soc. 41, 594 (2002)

    Google Scholar 

  18. Mostafazadelh A: Dynamical Invariant, Adiabatic Approximation and the Geometric Phase. Nova, Science Pub., New York (2001)

    Google Scholar 

  19. Dodonov V.V., Manko V.I.: Coherent states and the resonance of a quantum damped oscillator. Phys. Rev. A 20, 550 (1979)

    Article  Google Scholar 

  20. Cervero J.M., Villarel J.: On the quantum theory of the damped harmonic oscillator. J. Phys. A. Math. Gen 17, 2963 (1984)

    Article  Google Scholar 

  21. Kim J.K., Kim S.P.: One parameter squeezed gaussian states of a time dependent harmonic oscillator and the selection rule for vacuum states. J. Phys. A. 32, 2711 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kim S. P.: Time-dependent displaced and squeezed number states. J. Phys. A. 36, 12089 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kim S.P., Page D.N.: Classical and quantum action-phase variables for time-dependent oscillators. Phys. Rev. A. 64, 012204 (2001)

    MathSciNet  Google Scholar 

  24. Mizrahi M.M.: Phase space path integrals, without limiting procedure. J. Math. Phys. 19, 298 (1978)

    Article  MathSciNet  Google Scholar 

  25. Ikot, A.N.: M.Sc. thesis, Department of Physics, University of Calabar, Calabar, Nigeria (2005)

  26. Ikot A.N., Ituen E.E., Essien I.E., Akpabio L.E.: Path integrals evaluation of a time dependent oscillator in an external field. Turk. J. Phys. 32, 305 (2008)

    Google Scholar 

  27. Sabir M., Rajagopalan S.: Path integral analysis of harmonic oscillator with time-dependent mass. Pramana. J. Phys. 37, 253 (1991)

    Article  Google Scholar 

  28. Ikot A.N., Uwah E.J., Akpabio L.E., Akpan I.O.: On the memory of non-locally damped harmonic oscillator. Afr. J. Math. Phys. 8, 43 (2010)

    MATH  Google Scholar 

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Correspondence to Akpan N. Ikot.

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Ikot, A.N., Akpabio, L.E. & Antia, A.D. Path Integral of Time-Dependent Modified Caldirola–Kanai Oscillator. Arab J Sci Eng 37, 217–224 (2012). https://doi.org/10.1007/s13369-011-0160-7

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  • DOI: https://doi.org/10.1007/s13369-011-0160-7

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