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TMF, 1974, Volume 21, Number 1, Pages 37–48 (Mi tmf3855)  

This article is cited in 5 scientific papers (total in 5 papers)

Singular quasipotential equation

V. Sh. Gogokhiya, A. T. Filippov


Abstract: A study is made of the quasipotential equation for the partial-wave scattering amplitude in momentum space. For singular quasipotentials $V(r)=gr^{-2n+1}$ ($n$ integral, greater than or equal to 1) the integral equation reduces to an inhomogeneous differential equation of order $2n$ with definite boundary conditions. For $n=2$, $l>0$, the existence and uniqueness of the solution of the corresponding boundary-value problem is proved. It is proposed to construct the solution in the $S$-wave case ($l=0$) by analytic continuation in $l$. It is shown that the solution obtained in this manner satisfies an integral equation with a potential that differs from the analytic continuation in $l$ of the original polynomial by a definite polynomial. The solutions that are found can be represented as series in powers of $g^\nu(\ln g)^{n_\nu}$ (modified perturbation theory). An approximate method of investigating quasipotentials with arbitrary (nonintegral) $n$ is proposed.

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English version:
Theoretical and Mathematical Physics, 1974, 21:1, 954–962

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Received: 20.11.1973

Citation: V. Sh. Gogokhiya, A. T. Filippov, “Singular quasipotential equation”, TMF, 21:1 (1974), 37–48; Theoret. and Math. Phys., 21:1 (1974), 954–962

Citation in format AMSBIB
\Bibitem{GogFil74}
\by V.~Sh.~Gogokhiya, A.~T.~Filippov
\paper Singular quasipotential equation
\jour TMF
\yr 1974
\vol 21
\issue 1
\pages 37--48
\mathnet{http://mi.mathnet.ru/tmf3855}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464972}
\zmath{https://zbmath.org/?q=an:0307.31004}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 21
\issue 1
\pages 954--962
\crossref{https://doi.org/10.1007/BF01035592}


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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. V. A. Gribov, “Amplitude of scattering at high energies on a singular potential of power type”, Theoret. and Math. Phys., 26:1 (1976), 31–38  mathnet  crossref
    2. V. Sh. Gogokhiya, D. P. Mavlo, A. T. Filippov, “Solution of a singular quasipotential equation for bound states”, Theoret. and Math. Phys., 27:3 (1976), 513–522  mathnet  crossref
    3. V. Sh. Gogokhiya, “Reduction of quasipotential equations to Sturm–Liouville problems and the comparison equation method”, Theoret. and Math. Phys., 48:1 (1981), 617–623  mathnet  crossref  mathscinet  isi
    4. V. N. Kapshai, S. P. Kuleshov, N. B. Skachkov, “On a class of exact solutions of quasipotential equations”, Theoret. and Math. Phys., 55:3 (1983), 545–553  mathnet  crossref  mathscinet  isi
    5. V. Sh. Gogokhiya, ““Fall toward the centre” in quasipotential theory”, Theoret. and Math. Phys., 59:1 (1984), 357–364  mathnet  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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