Skip to main content
Log in

Few-body problem in the boundary condition model and quasipotentials

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

The boundary condition model is reformulated in terms of singular quasipotentials. In the three-body problem, Fredholm integral equations are constructed for the densities of simple and double layers concentrated on a noncompact surface with edges. Differential equations augmented with two-sided boundary conditions are formulated for the Faddeev and Faddeev—Yakubovskii components of the wave functions of three- and four-body systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Breit and W. G. Boricious,Phys. Rev.,75, 1029 (1949).

    Google Scholar 

  2. H. Feshbach and E. L. Lomon,Phys. Rev.,102, 891 (1956).

    Google Scholar 

  3. Y. E. Kim and A. Tubis,Phys. Rev. C,1, 414 (1970).

    Google Scholar 

  4. D. D. Brayshaw,Phys. Rev. C,3, 35 (1971).

    Google Scholar 

  5. V. B. Belyaev and A. L. Zubarev,Physica (Utrecht),3, 77 (1971).

    Google Scholar 

  6. Y. E. Kim and A. Tubis,Phys. Rev. C,4, 693 (1971).

    Google Scholar 

  7. D. D. Brayshaw,Phys. Rev. D,7, 1835 (1973).

    Google Scholar 

  8. V. Efimov,Yad. Fiz.,10, 107 (1969).

    Google Scholar 

  9. V. N. Efimov and G. Shults,Fiz. Elem. Chastits At. Yadra,7, 875 (1976).

    Google Scholar 

  10. V. E. Kuz'michev and V. F. Kharchenko,Teor. Mat. Fiz.,31, 75 (1977).

    Google Scholar 

  11. S. P. Merkuriev and A. K. Motovilov,Lett. Math. Phys.,7, 497 (1983).

    Google Scholar 

  12. S. P. Merkur'ev and A. K. Motovilov,Theory of Quantum Systems with Strong Interaction [in Russian], Kalinin (1983).

  13. A. K. Motovilov,Vestn. Leningr. Univ., No. 22, 76 (1983).

    Google Scholar 

  14. S. P. Merkur'ev and A. K. Motovilov,The Few-Body Problem in Physics. Ninth European Conference [in Russian], Tbilisi (1984), p. 48.

  15. A. K. Motovilov, “The quantum three-body problem in the boundary condition model,”Candidate's Dissertation [in Russian], Leningrad State University, Leningrad (1984).

    Google Scholar 

  16. A. A. Krivitskii, Yu. A. Kuperin, S. P. Merkur'ev, A. K. Motovilov, and S. L. Yakovlev,Fiz. Elem. Chastits At. Yadra,17, 267 (1986).

    Google Scholar 

  17. L. D. Faddeev,Tr. Mosk. Inst. Akad. Nauk SSSR,69, 1 (1963).

    Google Scholar 

  18. E. L. Lomon and M. McMillan,Ann. Phys. (N. Y.),23, 439 (1963).

    Google Scholar 

  19. M. M. Hoenig and E. L. Lomon,Ann. Phys. (N. Y.),36, 363 (1966).

    Google Scholar 

  20. M. M. Hoening,Phys. Rev. C,3, 1118 (1971).

    Google Scholar 

  21. S. P. Merkur'ev and S. L. Yakovlev,Teor. Mat. Fiz.,56, 60 (1983).

    Google Scholar 

  22. S. P. Merkuriev, C. Gignoux, and A. Lavern,Ann. Phys. (N. Y.),99, 30 (1976).

    Google Scholar 

  23. S. P. Merkuriev, S. L. Yakovlev, and C. Gignoux,Nucl. Phys.,431, 125 (1984).

    Google Scholar 

  24. B. Schulze and G. Wildenhain,Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebiger Ordnung, Academie-Verlag, Berlin (1977).

    Google Scholar 

  25. V. S. Vladimirov,Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

Download references

Authors

Additional information

St Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 435–447, March, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merkur'ev, S.P., Motovilov, A.K. & Yakovlev, S.D. Few-body problem in the boundary condition model and quasipotentials. Theor Math Phys 94, 306–314 (1993). https://doi.org/10.1007/BF01017263

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01017263

Keywords

Navigation