Skip to main content
SpringerLink
Log in

On the finiteness of the discrete spectrum of Hamiltonians for quantum systems of three one- or two-dimensional particles

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

The system of three particles (acting in K dimensions (K=1, 2)) without stable two-particle subsystems is studied. For short-range potentials V ij (r ij ), the finiteness of the discrete spectrum is proved for any type of permutational symmetry.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. VugalterS. A. and ZhislinG. M., Teor. Mat. Fiz. 55, 269–281 (1983) (in Russian).

    Google Scholar 

  2. ZhislinG. M., Teor. Mat. Fiz. 21, 60–73 (1974) (in Russian).

    Google Scholar 

  3. AntonetsM. A., ZhislinG. M., and ShereshevskyI. A., Appendix to the book V. Jörgens and I. Veidman, Spectral Properties of Hamiltonian Operators, Mir, Moscow, 1976 (in Russian).

    Google Scholar 

  4. BirmanM. A., Mat. Sbornik 55, 125–173 (1961) (in Russian).

    Google Scholar 

  5. VugalterS. A. and ZhislinG. M., Dokl. Akad. Nauk USSR 317, 1365 (1991) (in Russian).

    Google Scholar 

  6. CyconH. L., FroeseR. G., KirschW., and SimonB., Schrödinger Operators, Springer-Verlag, New York, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Steklov Institute of Mathematics, Fontanka 27, 191011, St. Petersburg, Russia

    S. A. Vugalter

  2. Radiophysical Research Institute, Lyadov St 25/14, 603600, N. Novgorod, Russia

    G. M. Zhislin

Authors
  1. S. A. Vugalter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Zhislin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vugalter, S.A., Zhislin, G.M. On the finiteness of the discrete spectrum of Hamiltonians for quantum systems of three one- or two-dimensional particles. Letters in Mathematical Physics 25, 299–306 (1992). https://doi.org/10.1007/BF00398402

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00398402

Mathematics Subject Classification (1991)

Search

Navigation