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Faddeev differential equations as a spectral problem for a nonsymmetric operator

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Abstract

We consider a nonsymmetric matrix operator whose eigenvalue problem is the system of Faddeev differential equations for a three-particle system. For this operator and its adjoint, the resolvents are represented in terms of Faddeev T-matrix components of the three-particle Schrödinger operator. On the basis of these representations, the invariant spaces of the operators under consideration are investigated and their eigenfunctions are determined. The biorthogonality and completeness of the eigenfunction system are proved.

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References

  1. R. Newton,Scattering Theory of Waves and Particles, McGraw-Hill, New York (1966).

    Google Scholar 

  2. L. D. Faddeev,Tr. Mat. Inst. Akad. Nauk SSSR,69, 1–125 (1963).

    Google Scholar 

  3. S. P. Merkuriev,Teor. Mat. Fiz.,32, 187 (1977).

    Google Scholar 

  4. S. P. Merkuriev,Yad. Fiz.,24, 289 (1976).

    Google Scholar 

  5. S. P. Merkuriev,Zap. Nauchn. Sem. LOMI,77, 148 (1978).

    Google Scholar 

  6. S. P. Merkuriev,Dokl. Akad. Nauk SSSR,241, 68 (1978).

    Google Scholar 

  7. S. P. Merkuriev,Teor. Mat. Fiz.,38, 201 (1979).

    Google Scholar 

  8. S. P. Merkuriev,Lett. Math. Phys.,3, 141 (1979).

    Google Scholar 

  9. S. P. Merkuriev,Ann. Phys.,130, 395 (1980).

    Google Scholar 

  10. S. P. Merkuriev and L. D. Faddeev,Quantum Scattering Theory for Multi-Particle Systems [in Russian], Moscow, Nauka (1985).

    Google Scholar 

  11. H. P. Noyes and H. Fiedeldey, in:Three Particle Scattering in Quantum Mechanics (J. Gillespie and J. Nuttal, eds.), New York (1968)

  12. S. P. Merkuriev, C. Gignoux, and A. Laverne,Ann. Phys.,99, 20 (1976).

    Google Scholar 

  13. S. K. Adhikari and W. Glöckle,Phys. Rev.,C19, 616 (1979).

    Google Scholar 

  14. J. F. Friar, B. F. Gibson, and G. L. Paine,Phys. Rev.,C22, 284 (1980).

    Google Scholar 

  15. V. V. Pupyshev,Teor. Mat. Fiz.,81, 86 (1989);Phys. Lett.,A140, 284 (1989).

    Google Scholar 

  16. J. W. Evans and D. K. Hoffman,J. Math. Phys.,22, 2858 (1981).

    Google Scholar 

  17. S. L. Yakovlev,Teor. Mat. Fiz.,102, 323 (1995).

    Google Scholar 

  18. V. I. Smirnov,A Course in Higher Mathematics [in Russian], Vol. 5, OGIZ, Moscow (1947).

  19. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. II,Fourier Analysis, Self-Adjointness. Academic Press, New York (1975).

    Google Scholar 

  20. W. Glöckle,Nucl. Phys. A141, 620 (1970).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, USSR

    S. L. Yakovlev

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  1. S. L. Yakovlev
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We dedicate this paper to the memory of Stanislav Petrovitch Merkuriev, who left us three years ago.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 3, pp. 513–528, June, 1996.

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Yakovlev, S.L. Faddeev differential equations as a spectral problem for a nonsymmetric operator. Theor Math Phys 107, 835–847 (1996). https://doi.org/10.1007/BF02070389

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  • DOI: https://doi.org/10.1007/BF02070389

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