RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
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


TMF, 1973, Volume 15, Number 3, Pages 353–366 (Mi tmf3675)  

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

Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential

V. B. Matveev


Abstract: A study is made of the Schrödinger equation on a half,axis with a potential $q(x)$ that is not absolutely integrable and may be unbounded at infinity. The main result of the paper is the proof of the existence and completeness of the wave operators $W_{\pm}(H,H_0)$ under the condition that the Fourier transform of the potential at the upper limit converges sufficiently fast everywhere except at a certain discrete set of points $k_j$. It is also proved that for such potentials eigenvalues in the continuous spectrum can appear only at the points $\lambda_j=k_j^2/4$.

Full text: PDF file (1542 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1973, 15:3, 574–583

Received: 17.04.1972

Citation: V. B. Matveev, “Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential”, TMF, 15:3 (1973), 353–366; Theoret. and Math. Phys., 15:3 (1973), 574–583

Citation in format AMSBIB
\Bibitem{Mat73}
\by V.~B.~Matveev
\paper Wave operators and positive eigenvalues for a Schr\"odinger equation with oscillating potential
\jour TMF
\yr 1973
\vol 15
\issue 3
\pages 353--366
\mathnet{http://mi.mathnet.ru/tmf3675}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 15
\issue 3
\pages 574--583
\crossref{https://doi.org/10.1007/BF01094564}


Linking options:
  • http://mi.mathnet.ru/eng/tmf3675
  • http://mi.mathnet.ru/eng/tmf/v15/i3/p353

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. B. Khasanov, “Eigenvalues of the Dirac operator in the continuous spectrum”, Theoret. and Math. Phys., 99:1 (1994), 396–401  mathnet  crossref  mathscinet  zmath  isi
    2. S. N. Naboko, A. B. Pushnitskii, “Point Spectrum on a Continuous Spectrum for Weakly Perturbed Stark Type Operators”, Funct. Anal. Appl., 29:4 (1995), 248–257  mathnet  crossref  mathscinet  zmath  isi
    3. V. B. Matveev, “Positons: Slowly Decreasing Analogues of Solitons”, Theoret. and Math. Phys., 131:1 (2002), 483–497  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:217
    Full text:74
    References:16
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019