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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 67, Issue 4

Issues

Finiteness of the discrete spectrum in a three-body system with point interaction

Kazushi Yoshitomi
  • Department of Mathematics and Information Sciences Tokyo Metropolitan University Minamiohsawa 1-1, Hachioji Tokyo 192-0397 Japan
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Published Online: 2017-07-14 | DOI: https://doi.org/10.1515/ms-2017-0030

Abstract

In this paper we are concerned with a three-body system with point interaction, which is called the Ter-Martirosian–Skornyakov extension. We locate the bottom of the essential spectrum of that system and establish the finiteness of the discrete spectrum below the bottom. Our work here refines the result of [MINLOS, R. A.: On point-like interaction between n fermions and another particle, Mosc. Math. J. 11 (2011), 113–127], where the semi-boundedness of the operator is obtained.

MSC 2010: Primary 81Q10; Secondary 35J10; 35P05; 81Q15

Keywords: three-body system; Ter-Martirosian–Skornyakov extension; point interaction; discrete spectrum

References

  • [1]

    Albeverio, S.—Kurasov, P.: Singular Perturbation of Differential Operators: Solvable Schrödinger Type Operators, London Math. Soc. Lecture Note Ser. Vol. 271, Cambridge University Press, Cambridge, 2000.Google Scholar

  • [2]

    Amrein, W. O.: Hilbert Space Methods in Quantum Mechanics, EPFL Press, Lausanne, 2009.Google Scholar

  • [3]

    Amrein, W. O.—Jauch, J. M.—Sinha, K. B.: Scattering Theory in Quantum Mechanics. Lecture notes and supplements in physics, No.16, W. A. Benjamin, Inc., Massachusetts, 1977.Google Scholar

  • [4]

    Blank, J.—Exner, P.—Havliček, M.: Hilbert Space Operators in Quantum Physics, Second edition, Springer, New York, 2008.Google Scholar

  • [5]

    Correggi, M.—Dell’antonio, G. F.—Finco, D.—Michelangeli, A. —Teta, A.: Stability for a system of N fermions plus a different particle with zero-range interactions, Rev. Math. Phys. 24 (2012), 1250017, 32 pp.CrossrefGoogle Scholar

  • [6]

    Dell’antonio, G. F.—Figari, R.—Teta, A.: Hamiltonians for systems of N particles interacting through point interaction, Ann. Inst. Henri Poincaré Phys. Théor. 60 (1994), 253–290.Google Scholar

  • [7]

    Finco, D.—Teta, A.: Quadratic forms for the fermionic unitary gas model, Rep. Math. Phys. 69 (2012), 131–159.CrossrefGoogle Scholar

  • [8]

    Minlos, R.: On point-like interaction between n fermions and another particle, Mosc. Math. J. 11 (2011), 113–127.Google Scholar

  • [9]

    Minlos, R.: A system of three pointwise interacting quantum particles, Russian Math. Surveys 69 (2014), 539–564.Google Scholar

  • [10]

    Minlos, R.—Shermatov, M. K.: Point interaction of three particles, Moscow Univ. Math. Bull. 44(6) (1989), 7–15.Google Scholar

  • [11]

    Mizohata, S.: The Theory of Partial Differential Equations, Cambridge Univ. Press, London, 1973.Google Scholar

  • [12]

    Schechter, M.: Operator Methods in Quantum Mechanics, Dover Publications, Inc., Mineola, New York, 2002.Google Scholar

About the article


Received: 2015-05-30

Accepted: 2016-03-30

Published Online: 2017-07-14

Published in Print: 2017-08-28


Citation Information: Mathematica Slovaca, Volume 67, Issue 4, Pages 1031–1042, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0030.

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