RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 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

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

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.

Full text: PDF file (1520 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tmf3855
• http://mi.mathnet.ru/eng/tmf/v21/i1/p37

 SHARE:

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
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
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
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
5. V. Sh. Gogokhiya, ““Fall toward the centre” in quasipotential theory”, Theoret. and Math. Phys., 59:1 (1984), 357–364
•  Number of views: This page: 244 Full text: 80 References: 29 First page: 1