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TMF, 2018, Volume 194, Number 2, Pages 364–380 (Mi tmf9343)  

This article is cited in 3 scientific papers (total in 3 papers)

Using the evolution operator method to describe a particle in a homogeneous alternating field

Sh. M. Nagiyev

Institute of Physics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Abstract: Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass $M(t)$ and a nonrelativistic particle with a variable mass $M(t)$ in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.

Keywords: nonrelativistic particle, linear potential, evolution operator, coherent state, oscillatory state, Wigner function.

Funding Agency Grant Number
Science Development Foundation under the President of the Republic of Azerbaijan EIF-KETPL-2-2015-1(25)-56/02/1
This research was supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EIF-KETPL-2-2015-1(25)-56/02/1).


DOI: https://doi.org/10.4213/tmf9343

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English version:
Theoretical and Mathematical Physics, 2018, 194:2, 313–327

Bibliographic databases:

PACS: 03.65.-w, 03.65.Fd
MSC: PACS numbers: 03.65.-w, 03.65.Fd
Received: 27.12.2016

Citation: Sh. M. Nagiyev, “Using the evolution operator method to describe a particle in a homogeneous alternating field”, TMF, 194:2 (2018), 364–380; Theoret. and Math. Phys., 194:2 (2018), 313–327

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nagiyev Sh.M., Ahmadov A.I., Amirova Sh.A., “On a Time Evolution of the Quadratic Quantum Systems.II”, Proceedings of the 6Th International Conference on Control and Optimization With Industrial Applications, Vol i, eds. Fikret A., Tamer B., Baku State Univ, Inst Applied Mathematics, 2018, 294–296  isi
    2. Sh. M. Nagiyev, A. I. Akhmedov, “Time evolution of quadratic quantum systems: Evolution operators, propagators, and invariants”, Theoret. and Math. Phys., 198:3 (2019), 392–411  mathnet  crossref  crossref  adsnasa  isi  elib
    3. Nagiyev Sh.M. Ahmadov A.I. Tarverdiyeva V.A. Amirova Sh.A., “Regarding Nonstationary Quadratic Quantum Systems”, Russ. Phys. J., 61:12 (2019), 2173–2187  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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