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TMF, 2010, Volume 162, Number 3, Pages 345–380 (Mi tmf6475)  

This article is cited in 16 scientific papers (total in 16 papers)

Time reversal for modified oscillators

R. Cordero-Soto, S. K. Suslov

School of Mathematical and Statistical Sciences; Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, USA

Abstract: We consider a new completely integrable case of the time-dependent Schrödinger equation in $\mathbb R^n$ with variable coefficients for a modified oscillator that is dual (with respect to time reversal) to a model of the quantum oscillator. We find a second pair of dual Hamiltonians in the momentum representation. The examples considered show that in mathematical physics and quantum mechanics, a change in the time direction may require a total change of the system dynamics to return the system to its original quantum state. We obtain particular solutions of the corresponding nonlinear Schrödinger equations. We also consider a Hamiltonian structure of the classical integrable problem and its quantization.

Keywords: Cauchy initial value problem, Schrödinger equation with variable coefficients, Green's function, propagator, time reversal, hyperspherical harmonic, nonlinear Schrödinger equation

DOI: https://doi.org/10.4213/tmf6475

Full text: PDF file (744 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 162:3, 286–316

Bibliographic databases:

Received: 11.06.2009

Citation: R. Cordero-Soto, S. K. Suslov, “Time reversal for modified oscillators”, TMF, 162:3 (2010), 345–380; Theoret. and Math. Phys., 162:3 (2010), 286–316

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v162/i3/p345

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Cordero-Soto R., Suazo E., Suslov S.K., “Quantum integrals of motion for variable quadratic Hamiltonians”, Ann. Physics, 325:9 (2010), 1884–1912  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Suslov S.K., “Dynamical invariants for variable quadratic Hamiltonians”, Phys. Scripta, 81:5 (2010), 055006, 11 pp.  crossref  zmath  adsnasa  isi  elib  scopus
    3. Cordero-Soto R., Suslov S.K., “The degenerate parametric oscillator and Ince's equation”, J. Phys. A, 44:1 (2011), 015101, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Lanfear N., Lopez R.M., Suslov S.K., “Exact wave functions for generalized harmonic oscillators”, J. Russ. Laser Res., 32:4 (2011), 352–361  crossref  isi  elib  scopus
    5. Sanborn B., Suslov S.K., Vinet L., “Dynamic invariants and the berry phase for generalized driven harmonic oscillators”, J. Russ. Laser Res., 32:5 (2011), 486–494  crossref  isi  elib  scopus
    6. Suazo E., Suslov S.K., Vega-Guzmán J.M., “The Riccati differential equation and a diffusion-type equation”, New York J. Math., 17A (2011), 225–244  mathscinet  zmath  isi
    7. Unal N., “Quasi-coherent states for harmonic oscillator with time-dependent parameters”, J. Math. Phys., 53:1 (2012), 012102  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Suazo E., Suslov S.K., “Soliton-like solutions for the nonlinear schrtsdinger equation with variable quadratic Hamiltonians”, J. Russ. Laser Res., 33:1 (2012), 63–83  crossref  isi  elib  scopus
    9. Suslov S.K., “On integrability of nonautonomous nonlinear Schrödinger equations”, Proc. Amer. Math. Soc., 140:9 (2012), 3067–3082  crossref  mathscinet  zmath  isi  elib  scopus
    10. Mahalov A., Suazo E., Suslov S.K., “Spiral Laser Beams in Inhomogeneous Media”, Opt. Lett., 38:15 (2013), 2763–2766  crossref  adsnasa  isi  elib  scopus
    11. Lopez R.M., Suslov S.K., Vega-Guzman J.M., “Reconstructing the Schrodinger Groups”, Phys. Scr., 87:3 (2013), 038112  crossref  zmath  adsnasa  isi  elib  scopus
    12. Acosta-Humanez P., Suazo E., “Liouvillian Propagators, Riccati Equation and Differential Galois Theory”, J. Phys. A-Math. Theor., 46:45 (2013), 455203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Schulze-Halberg A., Roy B., “Time Dependent Potentials Associated With Exceptional Orthogonal Polynomials”, J. Math. Phys., 55:12 (2014), 123506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    14. Koutschan Ch., Suazo E., Suslov S.K., “Fundamental Laser Modes in Paraxial Optics: From Computer Algebra and Simulations To Experimental Observation”, Appl. Phys. B-Lasers Opt., 121:3 (2015), 315–336  crossref  adsnasa  isi  elib  scopus
    15. 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
    16. Man'ko I V., Markovich L.A., “Quantum Tomography of Time-Dependent Nonlinear Hamiltonian Systems”, Rep. Math. Phys., 83:1 (2019), 87–106  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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