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Home > Journals > SCIREA Journal of Physics > Archive > Paper Information

Responses to Frequency Modulation in a Quantum Harmonic Oscillator

Volume 4, Issue 1, February 2019    |    PP. 8-16    |PDF (1074 K)|    Pub. Date: March 20, 2019
106 Downloads     741 Views  

Author(s)
Chang Jae Lee, Department of Nanochemistry, Sun Moon University, Asan 31460, Korea.

Abstract
A quantum harmonic oscillator with a frequency modulation is an extensively studied model, and has relevance to important physical processes. In this paper we consider response of the frequency modulation in terms of the time dependence of quasi energies and the deviation from the quantum virial theorem. Four modulation types\- linear, quadratic, exponential, and sinusoidal-are considered. In all cases the average potential and the average kinetic quasi-energies as well as the deviation from the quantum virial theorem exhibit oscillations in response to frequency modulation. A comparative study of the responses for these modulation types are given.

Keywords
Time-dependent harmonic oscillator, Frequency modulation, quasienergy, quantum virial theorem

Cite this paper
Chang Jae Lee, Responses to Frequency Modulation in a Quantum Harmonic Oscillator, SCIREA Journal of Physics. Vol. 4 , No. 1 , 2019 , pp. 8 - 16 .

References

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[ 2 ] Tobalina, A., Palmero, M., Martínez-Garaot, S., & Muga, J. G. (2017). Fast atom transport and launching in a nonrigid trap. Scientific reports, 7(1), 5753. doi:10.1038/s41598-017-05823-x.
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[ 5 ] Lewis, H. R. (1968). Class of exact invariants for classical and quantum time-dependent har- monic oscillators. J. Math. Phys., 9, 1976.
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[ 7 ] Pinney, E. (1950). The nonlinear differential equation y′′ + p(x)y + cy−3 = 0. Proc. of the American Math. Soc. 1, 681.
[ 8 ] Macedo, D. X. and Guedes, I. (2015). Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions, in Quantum Foundations and Open Quantum Systems: Lecture Notes of the Advanced School, (editors) Nieuwenhuizen, T., et al. World Scientific Publishing Co. Pte. Ltd., Singapore.
[ 9 ] See for example, Bayfield, J. E. (1999). Quantum Evolution: An Introduction to Time-Dependent Quantum Mechanics, Wiley, New York.
[ 10 ] The linear modulation case was considered in different contexts in: Lee, C. J. (2018). Dynamics of wave packet in a harmonic potential with linear frequency chirp. J. of Smart Technol., Vol. 3, No. 2 (in press).

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