Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 1, Pages 142–161
DOI: https://doi.org/10.4213/tmf6338 (Mi tmf6338) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Lie algebraic treatment of the quadratic invariants for a quantum system

M. Sebawe Abdallaa, P. G. L. Leachb

a Mathematics Department, College of Science, King Saud University
b School of Mathematical Sciences, University of KwaZulu-Natal
Full-text PDF (450 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf6338
Abstract: We consider the problem of the time-dependent degenerate parametric amplifier. We obtain the quadratic invariant and use it to derive the wave function via its $su(1,1)$ algebraic basis and a unitary transformation to the time-dependent Schrödinger equation for the parametric amplifier. We obtain the real and the complex invariants, which we use to solve the time-dependent Cauchy problem. Using different integrability conditions, we find the most general solution, which we analyze extensively, providing details of the calculations.
Keywords: wave function, Lie algebra.
Received: 08.05.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 1, Pages 535–550
DOI: https://doi.org/10.1007/s11232-009-0043-1
Bibliographic databases:
Language: Russian
Citation: M. Sebawe Abdalla, P. G. L. Leach, “Lie algebraic treatment of the quadratic invariants for a quantum system”, TMF, 159:1 (2009), 142–161; Theoret. and Math. Phys., 159:1 (2009), 535–550
Citation in format AMSBIB
\Bibitem{SebLea09}
\by M.~Sebawe~Abdalla, P.~G.~L.~Leach
\paper Lie algebraic treatment of the~quadratic invariants for a~quantum system
\jour TMF
\yr 2009
\vol 159
\issue 1
\pages 142--161
\mathnet{http://mi.mathnet.ru/tmf6338}
\crossref{https://doi.org/10.4213/tmf6338}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2547442}
\zmath{https://zbmath.org/?q=an:1174.81002}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...159..535A}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 159
\issue 1
\pages 535--550
\crossref{https://doi.org/10.1007/s11232-009-0043-1}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000269080400009}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70349540362}
Linking options:
  • https://www.mathnet.ru/eng/tmf6338
  • https://doi.org/10.4213/tmf6338
  • https://www.mathnet.ru/eng/tmf/v159/i1/p142
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:507
    Full-text PDF :206
    References:60
    First page:7
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024