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TMF, 1970, Volume 2, Number 3, Pages 367–376 (Mi tmf4043)  

This article is cited in 12 scientific papers (total in 13 papers)

Wave operators for the Schrödinger equation with a slowly decreasing potential

V. S. Buslaev, V. B. Matveev


Abstract: The present article is devoted to the study in space $L_2(R^n)$ of the energy operator $\displaystyle H_q=-\frac 1{2m}\Delta+q(x)$, where the function $q(x)$ decreases slower that $|x|^{-\alpha}$, $\alpha>0$, as $|x|\to\infty$. An explicit “regularizing” operator $U_q(t)$ is constructed and the existence of generalized wave operators
$$ W_{\pm}(H_q, H_0)=\mathop{\textrm{s-lim}}_{t\to\pm\infty}\exp\{-itH_q\}\exp\{itH_0\}U_q(t) $$
is proved.

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English version:
Theoretical and Mathematical Physics, 1970, 2:3, 266–274

Bibliographic databases:

Received: 31.07.1969

Citation: V. S. Buslaev, V. B. Matveev, “Wave operators for the Schrödinger equation with a slowly decreasing potential”, TMF, 2:3 (1970), 367–376; Theoret. and Math. Phys., 2:3 (1970), 266–274

Citation in format AMSBIB
\Bibitem{BusMat70}
\by V.~S.~Buslaev, V.~B.~Matveev
\paper Wave operators for the Schr\"odinger equation with a~slowly decreasing potential
\jour TMF
\yr 1970
\vol 2
\issue 3
\pages 367--376
\mathnet{http://mi.mathnet.ru/tmf4043}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473580}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 2
\issue 3
\pages 266--274
\crossref{https://doi.org/10.1007/BF01038047}


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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. P. P. Kulish, L. D. Faddeev, “Asymptotic conditions and infrared divergences in quantum electrodynamics”, Theoret. and Math. Phys., 4:2 (1970), 745–757  mathnet  crossref  zmath
    2. V. B. Matveev, “Invariance principle for generalized wave operators”, Theoret. and Math. Phys., 8:1 (1971), 663–667  mathnet  crossref  mathscinet  zmath
    3. L. A. Sakhnovich, “The invariance principle for generalized wave operators”, Funct. Anal. Appl., 5:1 (1971), 49–55  mathnet  crossref  mathscinet  zmath
    4. V. B. Matveev, M. M. Skriganov, “Scattering problem for radial Schrödinger equation with a slowly decreasing potential”, Theoret. and Math. Phys., 10:2 (1972), 156–164  mathnet  crossref  zmath
    5. L. A. Sakhnovich, “On allowing for all scattering channels in an $n$-body problem with Coulomb interaction”, Theoret. and Math. Phys., 13:3 (1972), 1239–1244  mathnet  crossref  mathscinet
    6. V. S. Buslaev, M. M. Skriganov, “Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation”, Theoret. and Math. Phys., 19:2 (1974), 465–476  mathnet  crossref  mathscinet  zmath
    7. S. N. Sokolov, “Separability and invariance in nonrelativstic and relativistic quantum mechanics”, Theoret. and Math. Phys., 23:3 (1975), 567–574  mathnet  crossref  mathscinet  zmath
    8. D. R. Yafaev, “On the asymptotic behavior of solutions of the time-dependent Schrödinger equation”, Math. USSR-Sb., 39:2 (1981), 169–188  mathnet  crossref  mathscinet  zmath  isi
    9. D. R. Yafaev, “Wave operators for the Schrödinger equation”, Theoret. and Math. Phys., 45:2 (1980), 992–998  mathnet  crossref  mathscinet  zmath  isi
    10. V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174  mathnet  crossref  mathscinet  zmath  isi  elib
    11. L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Sakhnovich L., “The Generalized Stationary Scattering Problems”, Complex Anal. Oper. Theory, 12:3 (2018), 607–613  crossref  isi
    13. Sakhnovich L., “The Generalized Scattering Problems: Ergodic Type Theorems”, Complex Anal. Oper. Theory, 12:3 (2018), 767–776  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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