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TMF, 2019, Volume 198, Number 3, Pages 451–472 (Mi tmf9524)  

This article is cited in 4 scientific papers (total in 4 papers)

Time evolution of quadratic quantum systems: Evolution operators, propagators, and invariants

Sh. M. Nagiyeva, A. I. Akhmedovb

a Institute of Physics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
b Baku State University, Institute of Physical Problems, Baku, Azerbaijan

Abstract: We use the evolution operator method to describe time-dependent quadratic quantum systems in the framework of nonrelativistic quantum mechanics. For simplicity, we consider a free particle with a variable mass $M(t)$, a particle with a variable mass $M(t)$ in an alternating homogeneous field, and a harmonic oscillator with a variable mass $M(t)$ and frequency $\omega(t)$ subject to a variable force $F(t)$. To construct the evolution operators for these systems in an explicit disentangled form, we use a simple technique to find the general solution of a certain class of differential and finite-difference nonstationary Schrödinger-type equations of motion and also the operator identities of the Baker–Campbell–Hausdorff type. With known evolution operators, we can easily find the most general form of the propagators, invariants of any order, and wave functions and establish a unitary relation between systems. Results known in the literature follow from the obtained general results as particular cases.

Keywords: nonstationary quadratic system, evolution operator, propagator, invariant, unitary relation.

Funding Agency Grant Number
Science Development Foundation under the President of the Republic of Azerbaijan EIF-KETPL-2-2015-1(2015)-1(25)-56/02/1
EIF/MQM/Elm-Tehsil-1-2016-1(26)-71/11/1
Бакинский государственный университет 50 + 50 (2018--2019)
This research is supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Research Grants Nos. EIF-KETPL-2-2015-1(2015)-1(25)-56/02/1 and EIF/MQM/Elm-Tehsil-1-2016-1(26)-71/11/1).
The research of A. I. Ahmadov is supported by Baku State University (Research Grants “50 + 50”, 2018–2019).


DOI: https://doi.org/10.4213/tmf9524

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English version:
Theoretical and Mathematical Physics, 2019, 198:3, 392–411

Bibliographic databases:

Received: 26.12.2017
Revised: 08.06.2018

Citation: Sh. M. Nagiyev, A. I. Akhmedov, “Time evolution of quadratic quantum systems: Evolution operators, propagators, and invariants”, TMF, 198:3 (2019), 451–472; Theoret. and Math. Phys., 198:3 (2019), 392–411

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Biswas K., Saha J.P., Patra P., “Squeezed Coherent State For Free-Falling Maxwell-Chern-Simons Model in Long-Wavelength Limit”, Indian J. Phys.  crossref  isi
    2. Patra P., Saha J.P., Biswas K., “Squeezed Coherent States For Gravitational Well in Noncommutative Space”, Indian J. Phys.  crossref  isi
    3. D. M. Tibaduiza, L. Pires, A. L. C. Rego, D. Szilard, C. Zarro, C. Farina, “Efficient algebraic solution for a time-dependent quantum harmonic oscillator”, Phys. Scr., 95:10 (2020), 105102  crossref  mathscinet  isi
    4. K. Zelaya, O. Rosas-Ortiz, “Quantum nonstationary oscillators: invariants, dynamical algebras and coherent states via point transformations”, Phys. Scr., 95:6 (2020), 064004  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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