General information
Latest issue
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

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


Full text: PDF file (744 kB)
References: PDF file   HTML file

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
\by R.~Cordero-Soto, S.~K.~Suslov
\paper Time reversal for modified oscillators
\jour TMF
\yr 2010
\vol 162
\issue 3
\pages 345--380
\jour Theoret. and Math. Phys.
\yr 2010
\vol 162
\issue 3
\pages 286--316

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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
    Number of views:
    This page:450
    Full text:115
    First page:10

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020